All questions
Question 1
Two populations of the same lizard species were measured for tail length (cm).
Population A tail lengths (cm): minimum 9, maximum 21
Population B tail lengths (cm): minimum 14, maximum 18
Which population shows more variation in tail length, based on range?
- Population B, because its minimum tail length is longer.
- Population A, because its tail lengths span a wider range of values. (correct answer)
- Both populations show the same variation because they are the same species.
- Neither population shows variation because each has a single minimum and maximum.
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). For example, data showing snail shell lengths: 10mm (2 individuals), 12mm (8), 14mm (25), 16mm (35), 18mm (20), 20mm (7), 22mm (3) reveals continuous variation with mean ~16mm, range 10-22mm, and normal distribution (most near middle, fewer at extremes)—clear evidence of variation within this snail population! Comparing the lizard populations, Population A has a range of 12 cm (21-9) while Population B has only 4 cm (18-14), so Population A shows greater spread in tail length variation. Choice B correctly analyzes the variation data by properly comparing the ranges and identifying Population A as having more variation due to its wider span of values. Choice A incorrectly picks Population B for having a longer minimum, but variation is about the overall spread, not just the starting point—always calculate range as max minus min to compare accurately! Reading variation from data—the data type approach: (1) RAW DATA (list of individual measurements): Count how many different values (shows variation). Find minimum and maximum (calculate range). Notice clustering (most near what value = mean estimate). Example: 150, 155, 160, 165, 165, 170, 170, 170, 175, 180 cm. Range: 180-150 = 30 cm. Most frequent: 170 cm (mode). Clear variation! (2) FREQUENCY TABLE (value, count): Read range (first to last value). Identify most frequent value (highest count = mode). Notice distribution shape (symmetric = normal, asymmetric = skewed). Example: Value 10 (n=3), 15 (n=12), 20 (n=25), 25 (n=10), 30 (n=2). Range: 10-30. Mode: 20 (most common). Bell-shaped (normal distribution). (3) GRAPH (histogram, bar chart): Read axes (trait on x, frequency/count on y). Observe shape (bell = normal continuous, separate bars = discrete). Identify spread (wide graph = high variation, narrow = low variation). Compare heights of bars (tallest = most common). All three data formats reveal variation—just need to read correctly! Comparing variation between populations: which has MORE variation? Population with WIDER range (larger max-min difference). Population with more SPREAD OUT distribution (flatter curve, less peaked). Population with more CATEGORIES (discrete variation). Example: Pop A heights 160-170 cm (range 10 cm, narrow), Pop B heights 140-190 cm (range 50 cm, wide). Pop B has more variation (5× wider range). More variation = more diversity = potentially more adaptability to changes!
Question 2
A biologist measured the beak depth (in mm) of 80 finches on one island and recorded the frequencies below. Which statement best describes the type of variation and the distribution pattern shown?
Beak depth (mm) → Number of finches
7 → 2
8 → 6
9 → 14
10 → 22
11 → 18
12 → 12
13 → 5
14 → 1
- Discrete variation with three distinct categories and no intermediates
- Continuous variation with most individuals near the middle values (approximately bell-shaped) (correct answer)
- No variation because all finches have similar beak depths
- Bimodal distribution with two equal peaks at 7 mm and 14 mm
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). Looking at the finch beak depth data: values range continuously from 7 mm to 14 mm with all intermediate values present (8, 9, 10, 11, 12, 13), and the frequency pattern shows most finches clustered around the middle values (10 mm has 22 finches, 11 mm has 18 finches) with fewer at the extremes (only 2 at 7 mm, only 1 at 14 mm)—this is the classic bell-shaped normal distribution of continuous variation! Choice B correctly identifies both the continuous nature of the variation (beak depths show a smooth range with intermediates) and the approximately bell-shaped distribution with most individuals near the middle values. Choice A incorrectly claims discrete variation when the data clearly shows continuous values, Choice C wrongly denies variation despite the 7 mm range, and Choice D misidentifies the pattern as bimodal when there's clearly one peak around 10-11 mm, not two equal peaks.
Question 3
A marine biologist measured shell length (mm) in a snail population. The smallest shell measured was 11 mm and the largest was 29 mm.
What is the range of shell length in this population sample?
- 18 mm (correct answer)
- 40 mm
- 11 mm
- 29 mm
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). For example, data showing snail shell lengths: 10mm (2 individuals), 12mm (8), 14mm (25), 16mm (35), 18mm (20), 20mm (7), 22mm (3) reveals continuous variation with mean ~16mm, range 10-22mm, and normal distribution (most near middle, fewer at extremes)—clear evidence of variation within this snail population! For the snail shell lengths, the summary gives a minimum of 11 mm and maximum of 29 mm, so the range is 29 - 11 = 18 mm, quantifying the variation in this continuous trait. Choice A correctly analyzes the data by calculating the range as 18 mm, directly from the given min and max. Choice B offers 40 mm, perhaps a miscalculation like adding instead of subtracting—always subtract min from max for range to get it right! When given summary stats like min and max, simply compute range as max - min (here 18 mm) to measure spread, and remember this indicates variation level—impressive work, you're honing your precision!
Question 4
A researcher counts the number of spots on 50 ladybugs. Results:
Spots → Number of ladybugs
- 0: 5
- 2: 9
- 4: 15
- 6: 14
- 8: 6
- 10: 1
Which statement best describes the variation in number of spots?
- Continuous variation, because spot number can take any value between 0 and 10.
- Discrete variation, because spot number is counted in whole-number categories. (correct answer)
- No variation, because most ladybugs have 4 or 6 spots.
- Bimodal variation, because there are exactly two spot-number categories.
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). For example, data showing snail shell lengths: 10mm (2 individuals), 12mm (8), 14mm (25), 16mm (35), 18mm (20), 20mm (7), 22mm (3) reveals continuous variation with mean ~16mm, range 10-22mm, and normal distribution (most near middle, fewer at extremes)—clear evidence of variation within this snail population! The ladybug spot data (0:5, 2:9, 4:15, 6:14, 8:6, 10:1) uses whole-number counts in distinct categories without fractions, showing discrete variation with a multimodal distribution centered around 4 and 6 spots. Choice B correctly analyzes the variation data by recognizing the discrete pattern where spots are counted in whole numbers, accurately describing the categorical nature. Choice A misidentifies it as continuous, but spot numbers don't have smooth intermediates like 1.5 spots—discrete traits are countable and categorical, so keep that distinction in mind! Reading variation from data—the data type approach: (1) RAW DATA (list of individual measurements): Count how many different values (shows variation). Find minimum and maximum (calculate range). Notice clustering (most near what value = mean estimate). Example: 150, 155, 160, 165, 165, 170, 170, 170, 175, 180 cm. Range: 180-150 = 30 cm. Most frequent: 170 cm (mode). Clear variation! (2) FREQUENCY TABLE (value, count): Read range (first to last value). Identify most frequent value (highest count = mode). Notice distribution shape (symmetric = normal, asymmetric = skewed). Example: Value 10 (n=3), 15 (n=12), 20 (n=25), 25 (n=10), 30 (n=2). Range: 10-30. Mode: 20 (most common). Bell-shaped (normal distribution). (3) GRAPH (histogram, bar chart): Read axes (trait on x, frequency/count on y). Observe shape (bell = normal continuous, separate bars = discrete). Identify spread (wide graph = high variation, narrow = low variation). Compare heights of bars (tallest = most common). All three data formats reveal variation—just need to read correctly! Comparing variation between populations: which has MORE variation? Population with WIDER range (larger max-min difference). Population with more SPREAD OUT distribution (flatter curve, less peaked). Population with more CATEGORIES (discrete variation). Example: Pop A heights 160-170 cm (range 10 cm, narrow), Pop B heights 140-190 cm (range 50 cm, wide). Pop B has more variation (5× wider range). More variation = more diversity = potentially more adaptability to changes!
Question 5
Two populations of the same plant species were measured for stem height.
Population A (cm): minimum 12, maximum 42
Population B (cm): minimum 18, maximum 28
Which statement is best supported by these data?
- Population B has greater variation in stem height because its minimum is higher
- Population A has greater variation in stem height because it has a wider range of values (correct answer)
- Both populations have the same variation because they are the same species
- Neither population shows variation because only minimum and maximum are listed
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). Comparing the two populations: Population A has a range of 42 - 12 = 30 cm, while Population B has a range of 28 - 18 = 10 cm, meaning Population A shows three times more variation in stem height. Choice B correctly identifies that Population A has greater variation because it has a wider range of values (30 cm vs 10 cm), demonstrating proper understanding of how range indicates variation level. Choice A incorrectly focuses on the minimum value rather than the range, C wrongly assumes same species means same variation (populations can differ!), and D misunderstands that minimum and maximum values are sufficient to calculate range and assess variation. When comparing variation between populations, always calculate and compare ranges—the population with the larger range has more variation, indicating greater diversity in that trait!
Question 6
Ten maple trees from the same population were measured for leaf length (cm):
9.2, 10.1, 10.4, 10.9, 11.3, 11.7, 12.0, 12.6, 12.9, 13.5
What is the range of leaf length in this sample?
- 4.3 cm (correct answer)
- 22.7 cm
- 13.5 cm
- 9.2 cm
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). For example, data showing snail shell lengths: 10mm (2 individuals), 12mm (8), 14mm (25), 16mm (35), 18mm (20), 20mm (7), 22mm (3) reveals continuous variation with mean ~16mm, range 10-22mm, and normal distribution (most near middle, fewer at extremes)—clear evidence of variation within this snail population! For this maple tree leaf length data, the raw measurements range from a minimum of 9.2 cm to a maximum of 13.5 cm, calculating to a range of 13.5 - 9.2 = 4.3 cm, showing continuous variation in this quantitative trait. Choice A correctly analyzes the variation data by accurately calculating the range as 4.3 cm, which quantifies the spread of differences among the trees. Choice C distracts by offering 13.5 cm, which is just the maximum, not the range—remember, range is max minus min, so double-check calculations to avoid this common mix-up! When working with raw data lists like this, sort the values to easily spot min and max (here 9.2 and 13.5), subtract for range, and notice the spread indicates variation—keep up the great work, you're getting better at this!
Question 7
A student recorded leaf lengths (cm) from 10 plants in the same population: 6.2, 6.4, 6.8, 7.1, 7.1, 7.5, 7.9, 8.0, 8.3, 8.6. What is the range of leaf length in this sample?
- 2.4 cm (correct answer)
- 14.8 cm
- 8.6 cm
- 6.2 cm
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). The leaf length data shows measurements from 6.2 cm to 8.6 cm, so the range calculation is: maximum value (8.6 cm) minus minimum value (6.2 cm) = 8.6 - 6.2 = 2.4 cm, which represents the total spread of variation in leaf length within this plant population sample. Choice A correctly calculates the range as 2.4 cm by subtracting the smallest value from the largest value (8.6 - 6.2 = 2.4), which is the standard formula for range in statistics. Choice B incorrectly adds all values or uses the wrong calculation; Choice C appears to be the maximum value alone rather than the range; Choice D is just the minimum value, not the range calculation. Reading variation from data—the data type approach: When given raw data (a list of individual measurements), the range is always calculated as Maximum - Minimum, which quantifies the total spread of variation—here, plants vary by 2.4 cm in leaf length, showing clear variation within the population! A larger range indicates more variation (more diversity in the trait), while a smaller range indicates less variation (individuals more similar to each other).
Question 8
Ten maple leaves from the same population were measured for leaf length (cm):
8.2, 9.0, 9.4, 10.1, 10.3, 10.7, 11.5, 11.9, 12.0, 12.6
What is the range of leaf length in this sample?
- 4.4 cm (correct answer)
- 12.6 cm
- 8.2 cm
- 20.8 cm
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). For example, data showing snail shell lengths: 10mm (2 individuals), 12mm (8), 14mm (25), 16mm (35), 18mm (20), 20mm (7), 22mm (3) reveals continuous variation with mean ~16mm, range 10-22mm, and normal distribution (most near middle, fewer at extremes)—clear evidence of variation within this snail population! In this maple leaf length data, the measurements range from a minimum of 8.2 cm to a maximum of 12.6 cm, so the range is 12.6 - 8.2 = 4.4 cm, highlighting the variation present. Choice A correctly calculates this range, while Choice B uses the maximum alone, which doesn't show spread—always subtract min from max for range. Practice with raw data lists by sorting values to find min and max quickly; great job verifying this, it builds strong analysis skills!
Question 9
A student measures leaf length (cm) from 10 plants in the same population:
3.2, 3.5, 3.7, 3.9, 4.0, 4.1, 4.4, 4.6, 4.8, 5.0
What is the range of leaf length in this sample?
- 1.8 cm (correct answer)
- 5.0 cm
- 3.2 cm
- 8.2 cm
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). The leaf length data shows measurements from 3.2 cm (minimum) to 5.0 cm (maximum), so the range calculation is: Range = Maximum - Minimum = 5.0 - 3.2 = 1.8 cm, indicating the spread of variation in this trait. Choice A correctly calculates the range as 1.8 cm by subtracting the smallest value from the largest value, which is the standard formula for range. Choices B (5.0 cm) simply states the maximum value rather than calculating range, C (3.2 cm) states the minimum value, and D (8.2 cm) incorrectly adds the values instead of subtracting them. Remember the range formula: Range = Maximum - Minimum. This simple calculation tells you how spread out the data is—a larger range means more variation in the population!
Question 10
A student measured leaf length for 10 plants in the same population (cm): 6, 7, 7, 8, 9, 9, 10, 11, 12, 12. What is the range of leaf length in this population?
- 5 cm
- 6 cm (correct answer)
- 12 cm
- 18 cm
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). For the leaf length data: 6, 7, 7, 8, 9, 9, 10, 11, 12, 12 cm, the minimum value is 6 cm and the maximum value is 12 cm, so the range = maximum - minimum = 12 - 6 = 6 cm, showing moderate variation in this plant population. Choice B correctly calculates the range as 6 cm by subtracting the minimum (6) from the maximum (12). Choice A incorrectly gives 5 cm (perhaps 11-6 or a calculation error), Choice C wrongly states 12 cm (the maximum value, not the range), and Choice D gives 18 cm which doesn't match any logical calculation from the data. Remember the range formula: always maximum minus minimum to measure the spread of variation!
Question 11
A class surveyed flower color in a population of wildflowers. Results are shown below.
Color morph | Number of plants
Red | 18
White | 7
Pink | 25
Which statement best describes the type of variation shown for flower color?
- Flower color shows continuous variation because the counts are different for each color.
- Flower color shows discrete variation because individuals fall into distinct categories. (correct answer)
- Flower color shows no variation because all plants have flowers.
- Flower color shows a normal (bell-shaped) distribution because pink is the most common.
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). For example, data showing snail shell lengths: 10mm (2 individuals), 12mm (8), 14mm (25), 16mm (35), 18mm (20), 20mm (7), 22mm (3) reveals continuous variation with mean ~16mm, range 10-22mm, and normal distribution (most near middle, fewer at extremes)—clear evidence of variation within this snail population! For this wildflower color data, the trait falls into three distinct categories—red (18 plants), white (7), pink (25)—with no intermediates, indicating discrete variation. Choice B correctly identifies this as discrete variation due to the clear, separate categories, while Choice A mistakenly calls it continuous just because counts differ—remember, continuous traits have gradients, not categories. When analyzing, look for whether traits blend or are distinct, and comparing to examples like blood types helps; you're doing great, keep building that skill!
Question 12
A bar graph shows fur color frequencies in a rabbit population (counts shown below):
- White: 18
- Gray: 44
- Black: 20
What does this graph show about variation in fur color in the population?
- Fur color shows continuous variation because the counts form a bell-shaped pattern.
- Fur color shows discrete variation because rabbits fall into distinct color categories. (correct answer)
- There is no variation because gray is the most common fur color.
- The range of fur color is 44−18=26 colors.
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). For example, data showing snail shell lengths: 10mm (2 individuals), 12mm (8), 14mm (25), 16mm (35), 18mm (20), 20mm (7), 22mm (3) reveals continuous variation with mean ~16mm, range 10-22mm, and normal distribution (most near middle, fewer at extremes)—clear evidence of variation within this snail population! The rabbit fur color bar graph shows three distinct categories—white (18), gray (44), black (20)—with no blending shades, indicating discrete variation in this qualitative trait. Choice B correctly analyzes the graph by recognizing the discrete variation with rabbits in distinct color categories. Choice A claims continuous with bell-shaped counts, but separate bars show categories, not a continuum—check for gaps versus smooth transitions to differentiate. For bar graphs, count the separate bars (here 3 colors) for discrete variation, and note frequencies don't form a bell unless it's a histogram for continuous data—wonderful progress, keep analyzing confidently!
Question 13
Two lizard populations were measured for tail length (cm).
Population A tail lengths (cm): 6.1, 6.4, 6.8, 7.0, 7.3, 7.9, 8.2, 8.5
Population B tail lengths (cm): 7.1, 7.2, 7.2, 7.3, 7.3, 7.4, 7.4, 7.5
Which population shows greater variation in tail length?
- Population B, because its values are closer to 7.3 cm.
- Population A, because it has a wider spread of values (larger range). (correct answer)
- Both populations show the same variation because they each have 8 measurements.
- Neither population shows variation because both have tail lengths near 7 cm.
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). For example, data showing snail shell lengths: 10mm (2 individuals), 12mm (8), 14mm (25), 16mm (35), 18mm (20), 20mm (7), 22mm (3) reveals continuous variation with mean ~16mm, range 10-22mm, and normal distribution (most near middle, fewer at extremes)—clear evidence of variation within this snail population! Comparing the lizard populations, Population A has tail lengths from 6.1 to 8.5 cm (range 2.4 cm) showing wider spread, while Population B is from 7.1 to 7.5 cm (range 0.4 cm) with values tightly clustered, so A has greater variation. Choice B correctly analyzes by identifying Population A with the larger range and wider spread, accurately comparing variation levels. Choice A incorrectly picks B for being closer to 7.3 cm, but closeness indicates less variation—remember, greater variation means more spread, not more centrality! To compare variation in raw data, calculate ranges (A: 8.5-6.1=2.4, B:7.5-7.1=0.4) and note the population with the wider range has more diversity—fantastic, you're mastering these comparisons!
Question 14
A genetics class recorded ABO blood types in a group of 80 students:
- Type A: 30
- Type B: 12
- Type AB: 6
- Type O: 32
Which statement is best supported by these data?
- Blood type shows continuous variation because there are many possible values.
- Blood type shows discrete variation because individuals fall into four distinct categories. (correct answer)
- There is no variation because type O is the most common.
- The range of blood types is 32−6=26.
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). For example, data showing snail shell lengths: 10mm (2 individuals), 12mm (8), 14mm (25), 16mm (35), 18mm (20), 20mm (7), 22mm (3) reveals continuous variation with mean ~16mm, range 10-22mm, and normal distribution (most near middle, fewer at extremes)—clear evidence of variation within this snail population! The blood type data divides into four distinct categories—A (30), B (12), AB (6), O (32)—with no intermediates, exemplifying discrete variation in this qualitative trait. Choice B correctly analyzes by identifying the discrete variation with four clear categories, supported by the data. Choice D incorrectly applies range to categories (32-6=26), but range is for continuous numerical data, not counts—use category count for discrete traits instead. In frequency data for traits like blood type, tally the number of distinct groups (here 4) to confirm discrete variation, unlike continuous which would show a spectrum—you're doing great, keep it up!
Question 15
A biologist measured beak depth (in mm) for 50 finches in one population and summarized the results below.
Beak depth (mm): 6 | 7 | 8 | 9 | 10 | 11 | 12
Number of finches: 2 | 6 | 12 | 15 | 9 | 4 | 2
Which statement best describes the variation in beak depth in this finch population?
- The finches show discrete variation because beak depth falls into only two categories (small vs. large).
- The finches show continuous variation, with most individuals near 9 mm and fewer at the extremes. (correct answer)
- There is no variation because all finches have beak depths between 6 and 12 mm.
- The distribution is bimodal because the highest counts occur at both 6 mm and 12 mm.
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). For example, data showing snail shell lengths: 10mm (2 individuals), 12mm (8), 14mm (25), 16mm (35), 18mm (20), 20mm (7), 22mm (3) reveals continuous variation with mean ~16mm, range 10-22mm, and normal distribution (most near middle, fewer at extremes)—clear evidence of variation within this snail population! In this finch beak depth data, the values range from 6 mm to 12 mm with frequencies peaking at 9 mm (15 finches) and decreasing toward the extremes (2 at 6 mm and 2 at 12 mm), showing a bell-shaped distribution typical of continuous variation. Choice B correctly analyzes the variation data by recognizing the continuous pattern with most individuals near 9 mm and fewer at the extremes, accurately describing the normal distribution. Choice C fails by denying variation despite the clear spread from 6 to 12 mm, while a good strategy is to always check the range and frequency peaks to confirm patterns like this—keep practicing, and you'll spot these easily!
Question 16
A student measures leaf length (cm) for 10 plants in the same population:
Plant IDs 1–10 leaf lengths (cm): 6.2, 5.9, 7.1, 6.8, 6.0, 7.4, 6.5, 5.7, 6.9, 6.1
What is the range of leaf length in this population?
- 1.7 cm (correct answer)
- 13.1 cm
- 0.6 cm
- 7.4 cm
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). For example, data showing snail shell lengths: 10mm (2 individuals), 12mm (8), 14mm (25), 16mm (35), 18mm (20), 20mm (7), 22mm (3) reveals continuous variation with mean ~16mm, range 10-22mm, and normal distribution (most near middle, fewer at extremes)—clear evidence of variation within this snail population! For this leaf-length data (5.7, 5.9, 6.0, 6.1, 6.2, 6.5, 6.8, 6.9, 7.1, 7.4 cm), the minimum is 5.7 cm and maximum is 7.4 cm, so the range is 7.4 - 5.7 = 1.7 cm, quantifying the spread of continuous variation in the population. Choice A correctly analyzes the variation data by accurately calculating the range as 1.7 cm, recognizing the differences among the individual measurements. A distractor like choice C might miscalculate the range (perhaps by subtracting wrong values), but always sort the data first to find true min and max—here, it's clearly 1.7 cm, showing variation exists even in this small sample! Reading variation from data—the data type approach: (1) RAW DATA (list of individual measurements): Count how many different values (shows variation). Find minimum and maximum (calculate range). Notice clustering (most near what value = mean estimate). Example: 150, 155, 160, 165, 165, 170, 170, 170, 175, 180 cm. Range: 180-150 = 30 cm. Most frequent: 170 cm (mode). Clear variation! (2) FREQUENCY TABLE (value, count): Read range (first to last value). Identify most frequent value (highest count = mode). Notice distribution shape (symmetric = normal, asymmetric = skewed). Example: Value 10 (n=3), 15 (n=12), 20 (n=25), 25 (n=10), 30 (n=2). Range: 10-30. Mode: 20 (most common). Bell-shaped (normal distribution). (3) GRAPH (histogram, bar chart): Read axes (trait on x, frequency/count on y). Observe shape (bell = normal continuous, separate bars = discrete). Identify spread (wide graph = high variation, narrow = low variation). Compare heights of bars (tallest = most common). All three data formats reveal variation—just need to read correctly! Comparing variation between populations: which has MORE variation? Population with WIDER range (larger max-min difference). Population with more SPREAD OUT distribution (flatter curve, less peaked). Population with more CATEGORIES (discrete variation). Example: Pop A heights 160-170 cm (range 10 cm, narrow), Pop B heights 140-190 cm (range 50 cm, wide). Pop B has more variation (5× wider range). More variation = more diversity = potentially more adaptability to changes!
Question 17
A histogram of shell length (mm) in a snail population shows most snails between 16–18 mm, fewer snails at 12–14 mm, and fewer snails at 20–22 mm. The overall range is 12–22 mm.
Which description best matches this shell-length variation?
- Discrete variation with separate categories and no intermediate values.
- Continuous variation with most individuals near the middle of the range. (correct answer)
- No variation because most individuals are between 16–18 mm.
- A perfectly uniform distribution because each shell length occurs equally often.
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). For example, data showing snail shell lengths: 10mm (2 individuals), 12mm (8), 14mm (25), 16mm (35), 18mm (20), 20mm (7), 22mm (3) reveals continuous variation with mean ~16mm, range 10-22mm, and normal distribution (most near middle, fewer at extremes)—clear evidence of variation within this snail population! The snail shell-length histogram describes a range of 10 mm (22-12) with most individuals between 16–18 mm and fewer at the extremes, indicating continuous variation in a bell-shaped distribution. Choice B correctly analyzes the variation data by identifying the continuous pattern and the central clustering, which matches the described normal distribution. Choice A mislabels it as discrete, but the smooth range with intermediates like 12–22 mm suggests continuous—histograms with connected bins often show continuous traits, so check for smooth gradients! Reading variation from data—the data type approach: (1) RAW DATA (list of individual measurements): Count how many different values (shows variation). Find minimum and maximum (calculate range). Notice clustering (most near what value = mean estimate). Example: 150, 155, 160, 165, 165, 170, 170, 170, 175, 180 cm. Range: 180-150 = 30 cm. Most frequent: 170 cm (mode). Clear variation! (2) FREQUENCY TABLE (value, count): Read range (first to last value). Identify most frequent value (highest count = mode). Notice distribution shape (symmetric = normal, asymmetric = skewed). Example: Value 10 (n=3), 15 (n=12), 20 (n=25), 25 (n=10), 30 (n=2). Range: 10-30. Mode: 20 (most common). Bell-shaped (normal distribution). (3) GRAPH (histogram, bar chart): Read axes (trait on x, frequency/count on y). Observe shape (bell = normal continuous, separate bars = discrete). Identify spread (wide graph = high variation, narrow = low variation). Compare heights of bars (tallest = most common). All three data formats reveal variation—just need to read correctly! Comparing variation between populations: which has MORE variation? Population with WIDER range (larger max-min difference). Population with more SPREAD OUT distribution (flatter curve, less peaked). Population with more CATEGORIES (discrete variation). Example: Pop A heights 160-170 cm (range 10 cm, narrow), Pop B heights 140-190 cm (range 50 cm, wide). Pop B has more variation (5× wider range). More variation = more diversity = potentially more adaptability to changes!
Question 18
In a population of 25 rabbits, fur color was recorded as:
- Brown: 11
- White: 9
- Black: 5
Which conclusion best describes the variation in fur color?
- Fur color shows discrete variation with three categories present in the population (correct answer)
- Fur color shows continuous variation because the numbers for each color are different
- There is no variation because brown is the most common color
- Fur color shows a normal (bell-shaped) distribution centered on white
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). The rabbit fur color data shows three distinct categories (Brown: 11, White: 9, Black: 5) with no intermediate colors like gray or tan mentioned—this is classic discrete variation where individuals fall into separate, non-overlapping categories. Choice A correctly identifies this as discrete variation with three categories present in the population, accurately recognizing that fur color occurs in distinct types rather than a continuous spectrum. Choice B incorrectly claims continuous variation, confusing different frequencies with continuous measurement, while choice C wrongly states no variation despite three different colors being present, and choice D misapplies the concept of normal distribution to categorical data. When identifying variation type, ask: Can you have intermediate values? For fur color, a rabbit is either brown, white, or black—not 'halfway between brown and white'—confirming discrete variation with clear categories!
Question 19
A biologist measures the wing length (in mm) of 12 finches from the same island population:
12, 14, 14, 15, 16, 16, 17, 18, 18, 19, 20, 21
Which statement best describes the type of variation shown for wing length in this population?
- Discrete variation, because wing length falls into only a few separate categories with no intermediate values
- No variation, because all finches have wing lengths close to 16 mm
- Continuous variation, because wing length shows a range of measurable values with intermediates (correct answer)
- Bimodal variation, because there are two equally high peaks at 14 mm and 18 mm
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). The finch wing length data shows values from 12 mm to 21 mm with many intermediate measurements (14, 15, 16, 17, 18, 19), demonstrating a smooth gradation of values rather than distinct categories—this is continuous variation with a range of 9 mm. Choice C correctly identifies this as continuous variation because wing length shows measurable values with intermediates between the minimum and maximum, which is the hallmark of continuous traits. Choice A incorrectly claims discrete variation, but the data clearly shows intermediate values (15, 17, 19) between the repeated values, while choice B wrongly states no variation despite the 9 mm range, and choice D incorrectly identifies a bimodal pattern when the data shows a relatively even distribution. When analyzing variation data, look for: (1) Do values fall into distinct categories (discrete) or show a smooth range (continuous)? (2) Are there intermediate values between the extremes? (3) Could you theoretically measure values between the recorded ones? For wing length, you could measure 15.5 mm or 16.3 mm—confirming continuous variation!
Question 20
A researcher measured beak depth (mm) in two bird populations.
Population 1: 8, 9, 9, 10, 10, 10, 11, 11
Population 2: 7, 8, 10, 12, 13, 14, 15, 16
Which population shows greater variation in beak depth, based on the data?
- Population 1, because more individuals are near 10 mm
- Population 2, because the values span a wider range (correct answer)
- Population 1, because it has repeated values
- They show the same variation because both have 8 measurements
Explanation: This question tests your ability to analyze population data to identify and describe variation—the differences among individuals in traits like height, color, size, or other characteristics. Population variation can be recognized and quantified from data in several ways: (1) RANGE shows the spread of variation (maximum value minus minimum value—if heights go from 150 cm to 190 cm, range = 40 cm, indicating substantial variation), (2) DISTRIBUTION PATTERN shows how trait values are distributed across the population, either CONTINUOUS VARIATION (trait shows smooth range with many intermediate values, often forming bell-shaped normal distribution where most individuals near the mean/average with fewer at extremes—example: height, weight, beak depth) or DISCRETE VARIATION (trait shows distinct categories with no intermediates—example: blood types A/B/AB/O, flower colors red/white/pink, four separate categories). (3) FREQUENCY DATA shows how many individuals have each trait value (histogram or frequency table), revealing whether variation is wide (many different values, spread out) or narrow (most individuals similar, clustered). Calculating ranges: Population 1 has beak depths from 8 mm to 11 mm (range = 11 - 8 = 3 mm), while Population 2 spans from 7 mm to 16 mm (range = 16 - 7 = 9 mm), making Population 2's range three times wider. Choice B correctly identifies Population 2 as having greater variation because the values span a wider range (9 mm vs 3 mm), demonstrating that range is the key measure of variation spread. Choice A incorrectly focuses on where values cluster rather than their spread, C wrongly equates repeated values with variation, and D falsely assumes sample size determines variation rather than the actual spread of values. Comparing variation: Always calculate range first! Population 2 (range = 9 mm) shows much more variation than Population 1 (range = 3 mm)—the wider spread indicates more diversity in beak depths, which could be important for adaptation!