Representing Data with Number Line Plots

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Statistics › Representing Data with Number Line Plots

Questions 1 - 10
1

A student measured the lengths (in cm) of 13 leaves: 6.2, 6.4, 6.5, 6.5, 6.6, 6.7, 6.8, 6.8, 6.9, 7.0, 7.1, 7.3, 7.6. Which plot best represents the data as a box plot summary (median and range only)?

Median = 6.7 cm; range = 1.4 cm.

Median = 6.9 cm; range = 1.3 cm.

Median = 6.8 cm; range = 1.4 cm.

Median = 6.8 cm; range = 1.3 cm.

Explanation

The plot is a box plot summarizing leaf lengths. Data values map to the median, quartiles, and min/max for the box and whiskers. Key features include median at 6.8 cm, box showing middle spread, and full spread of 1.4 cm from 6.2 to 7.6, with slight right skew. The correct answer A matches because for 13 values, the 7th is 6.8, and range is 7.6-6.2=1.4. A common misconception is to average middle values for odd number of data, but for odd, it's the middle one. To analyze, first check the scale for the length units. Then, count and sort the data to verify median and range.

2

A store recorded 18 customer wait times (in minutes): 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 9, 10, 12, 14. Which plot best represents the data as a histogram using bin width 5 minutes with bins 0–4, 5–9, 10–14?

Histogram counts: 0–4: 8, 5–9: 7, 10–14: 3.

Histogram counts: 0–4: 7, 5–9: 8, 10–14: 3.

Histogram counts: 0–4: 9, 5–9: 6, 10–14: 3.

Histogram counts: 0–4: 8, 5–9: 6, 10–14: 4.

Explanation

The plot is a histogram of wait times with bin width 5. Data values are counted into bins 0–4, 5–9, 10–14. Key features include high frequency in 0–4 with 8, decreasing to 3 in 10–14, spread from 1 to 14, right-skewed shape. The correct answer A matches because the counts are exactly 8,7,3 for the bins. A common misconception is to include boundary values in the wrong bin, like putting 5 in 0–4 instead of 5–9. To analyze, first check the scale and bin definitions. Then, count the points in each bin to confirm the heights.

3

A band director recorded the 20 practice times (in minutes) for students over a week: 5, 10, 10, 15, 15, 15, 20, 20, 20, 20, 25, 25, 30, 30, 35, 40, 45, 50, 55, 60. Which statement correctly describes the distribution shown by a histogram of these times?

The distribution is right-skewed because most times are near 10–30 with a tail of larger times up to 60.

The distribution is approximately symmetric because the values are evenly spread from 5 to 60.

The distribution has a gap between 20 and 25 because no times occur in that interval.

The distribution is left-skewed because most times are near 40–60 with a few small times near 5–15.

Explanation

The plot is a histogram of practice times. Data values are binned, with bars showing frequencies. Key features include cluster in lower times 10-30, spread from 5 to 60, right-skewed shape with long tail to higher times. The correct answer C matches because most are near 10–30 with a tail up to 60. A common misconception is to see it as uniform when there is clear skew due to the tail. To analyze, first check the scale and bin sizes. Then, count points per bin to see the distribution shape.

4

A teacher recorded 16 quiz scores (out of 20): 8, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 17, 18, 19. Which statement correctly describes the distribution shown by a histogram of these scores?

The distribution is strongly left-skewed because there are many high scores and only a few low scores.

The distribution is approximately symmetric because the scores increase gradually from 8 to 19 with similar counts in the middle.

The distribution has a gap between 13 and 14 because no scores occur in that interval.

The distribution is strongly right-skewed because there are many low scores and only a few high scores.

Explanation

The plot is a histogram of quiz scores. Data values are grouped into bins, with bar heights showing frequency in each bin. Key features include even distribution from 8 to 19, with clusters in the middle scores, spread of 11 points, and approximately symmetric shape. The correct answer B matches because the scores are balanced with gradual increase and similar counts around the center. A common misconception is to identify skew when the distribution is actually symmetric due to focusing on end bins only. To analyze, first check the scale and bin widths for proper grouping. Then, count data points in each bin to assess the shape and symmetry.

5

A club tracked how many push-ups 15 members completed in one minute: 14, 16, 18, 18, 19, 20, 20, 20, 21, 22, 22, 23, 24, 26, 28. Which statement correctly describes the distribution shown by a dot plot?

The distribution is left-skewed because most values are around 24–28 with a few smaller values near 14–16.

The distribution has a gap from 20 to 22 because no values occur in that interval.

The distribution is symmetric because the values are evenly balanced around 21 with equal tails.

The distribution is right-skewed because most values are around 18–23 with a few larger values near 26–28.

Explanation

The plot is a dot plot of push-up counts. Each count is mapped as a dot on the number line, stacked for repeats. Key features include cluster around 20 with 3 dots, spread from 14 to 28, and right-skewed shape with longer tail to the right. The correct answer A matches because most values are in 18–23, with few larger ones extending to 28. A common misconception is to identify the skew based on the wrong direction of the tail. To analyze, first check the scale to see the range of push-ups. Then, count the dots to determine clusters and skew.

6

Daily high temperatures (°F) over 14 days were: 62, 64, 65, 65, 66, 66, 67, 68, 68, 69, 70, 71, 72, 74. Which statement correctly describes the distribution shown by a box plot of these temperatures?

The median is 67°F, and the range is 12°F.

The median is 68.5°F, and the range is 10°F.

The median is 68°F, and the range is 10°F.

The median is 67.5°F, and the range is 12°F.

Explanation

The plot is a box plot, summarizing the temperature data. The data values map to the plot by calculating quartiles, median, and extremes for the box and whiskers. Key features include the median at 67.5°F, box from Q1 to Q3 showing middle 50%, and whiskers to min 62°F and max 74°F, with no outliers. The correct answer A matches because the median is the average of 7th and 8th values (67+68)/2=67.5, and range is 74-62=12. A common misconception is to take the median as one of the middle values instead of averaging for even number of data points. To analyze, first check the scale to see the range of temperatures. Then, count the data points and sort them to verify the median and range.

7

A cafeteria recorded the prices (in dollars) of 12 lunch items: 1.25, 1.50, 1.50, 1.75, 2.00, 2.00, 2.25, 2.50, 2.50, 2.75, 3.00, 3.25. Which plot best represents the data as a dot plot (each value shown as one dot above its price)?

Dots at: 1.25(1), 1.50(2), 1.75(1), 2.00(1), 2.25(1), 2.50(2), 2.75(2), 3.00(1), 3.25(1).

Dots at: 1.25(1), 1.50(2), 1.75(1), 2.00(2), 2.25(1), 2.50(1), 2.75(1), 3.00(1), 3.25(1).

Dots at: 1.25(1), 1.50(2), 1.75(1), 2.00(2), 2.25(1), 2.50(2), 2.75(1), 3.00(1), 3.25(1).

Dots at: 1.25(1), 1.50(1), 1.75(1), 2.00(2), 2.25(1), 2.50(2), 2.75(1), 3.00(1), 3.25(2).

Explanation

The plot is a dot plot, displaying prices on a number line. Each price is mapped by placing a dot above its value, stacking for duplicates. Key features include clusters at 1.50, 2.00, 2.50 with 2 dots each, spread from 1.25 to 3.25, and a fairly uniform shape with increasing prices. The correct answer A matches because it accurately lists the positions and counts of dots for each price in the data. A common misconception is to forget to stack dots for repeated values, leading to incorrect counts. To analyze, first check the scale on the number line for the price range. Then, count the dots at each price to match the frequency in the data set.

8

A PE teacher recorded the number of push-ups completed by 11 students in one minute: 14, 15, 15, 16, 16, 16, 17, 18, 18, 19, 21. Which plot best represents the data as a dot plot on a number line?

Dots at 14(1), 15(2), 16(2), 17(1), 18(2), 19(2), 21(1).

Dots at 14(2), 15(2), 16(3), 17(1), 18(1), 19(1), 21(1).

Dots at 14(1), 15(2), 16(3), 17(1), 18(2), 19(1), 21(1).

Dots at 14(1), 15(1), 16(3), 17(2), 18(2), 19(1), 21(1).

Explanation

A dot plot shows push-up counts as dots on a number line, with stacks like three at 16 and two at 15, 18. The data maps to dots at 14 (one), 15 (two), 16 (three), 17 (one), 18 (two), 19 (one), 21 (one), creating a cluster around 16 with tails. The plot features a peak at 16 and slight right skew to 21, spanning 14 to 21. Choice A correctly lists these frequencies for the visual representation. A common misconception is overlooking stacked dots as single points, but stacks indicate multiples. Check the number line scale from 14 to 21. Then, count dots per value to match the 11 students.

9

A cafeteria tracked the waiting times (in minutes) for 16 students: 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 10, 11. Which statement correctly describes the distribution when shown in a histogram with 2-minute bins: 2–3, 4–5, 6–7, 8–9, 10–11?

The histogram would be uniform because each bin has the same number of values.

The histogram would show a gap because there are no values in the 6–7 bin.

The histogram would be strongly left-skewed with most values in the 10–11 bin.

The histogram would show a cluster in the 6–7 bin and a smaller right tail toward 10–11.

Explanation

A histogram groups waiting times into 2-minute bins on a number line, with bar heights showing counts like one in 2–3, five in 4–5, five in 6–7, three in 8–9, and two in 10–11. Data values fall into bins, creating a visual of higher bars in the middle and tapering off, especially to the right. Key features include a cluster around 6–7 minutes with a right tail extending to 10–11, indicating slight right skew and spread from 3 to 11. Choice A correctly describes this cluster and tail, aligning with the bin frequencies. A common misconception is thinking empty bins mean gaps in data, but here all bins have values except possibly unused ones outside the range. First, check the bin scale to ensure intervals like 2–3 capture values correctly. Then, count entries per bin to match the total of 16 times.

10

The heights (in inches) of 10 plants in a classroom experiment were: 14, 15, 15, 16, 16, 17, 18, 18, 19, 22. Which statement correctly describes the distribution in a box plot of these data?

There is a gap between 18 and 19 inches that would appear as an empty space in a box plot.

The data are perfectly symmetric because the maximum and minimum are equally far from the median.

The distribution is left-skewed because most values are close to 22 inches.

The distribution is right-skewed because the upper end extends farther (up to 22) than the lower end.

Explanation

A box plot summarizes data on a number line using a box for the middle 50% and whiskers for the extremes. The plant heights map to min at 14, Q1 at 15, median at 16.5, Q3 at 18, and max at 22, with the box from 15 to 18 and whiskers extending outward. Key features include a compact lower half and a longer upper whisker, showing right-skewed shape with spread from 14 to 22 and a potential outlier feel at 22. Choice B correctly identifies the right skew due to the upper end extending farther to 22. A common misconception is confusing skew with symmetry based only on min-max distance, but skew is about tail length and data density. Always check the number line scale to locate quartiles precisely. Then, count data points in each section to verify the five-number summary.

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