AP Statistics : Data
Study concepts, example questions & explanations for AP Statistics
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Example Questions
Example Question #1 : How To Interpret Histograms
What is the best measurement of center and spread for the following data set represented by a histogram?
Mean and Interquartile Range
Mean and Standard Deviation
Median and Interquartile Range
Median and Standard Deviation
Mean and Range
Median and Interquartile Range
For skewed distributions, the outliers can greatly affect the value of the mean and the standard deviation. Therefore, the median and IQR would be better measures of center and spread because they are not greatly influenced by outlier values.
Example Question #1 : How To Interpret Histograms
Louie collects data on the amount of sleep students in his class get.
Below is a graphical representation of the data
Which of the following is/are false about Louie's class' data?
i: the student with 2 hours of sleep is an outlier
ii: without the student with 2 hours of sleep the data is roughly normally distributed
iii: without the student with 2 hours of sleep the data is slightly right skewed
iv: the student with 2 hours of sleep is within 2 standard deviations of the mean
ii & iv
i, ii & iii
ii, iii & iv
iii & iv
i & ii
ii & iv
Entering the data into a calculator you can quickly find the mean to be 6.5 and the sd to be 1.6 6.5-3.2=3.3 3.3>2 so iv is false and by virtue of this 2 is an outlier so i is true.
Between ii and iii, the data is not bell shaped, and does exhibit a slight right skew without the mentioned pt due to more density on 5 and 6 hours than 8 and 9
Example Question #1 : How To Interpret Histograms
Louie collected the following data on sleeping habits of his classmates:
Calculate the median, 1st and 3rd quartile (Q1 and Q3) and mode for the data. There are 19 students in the class.
Median:6 Q1:5 Q3:8 Mode:6
Median:7 Q1:6 Q3:9 Mode:8
Median:6 Q1:6 Q3:8 Mode:6
Median:7 Q1:6 Q3:8 Mode:6
Median:6 Q1:5 Q3:9 Mode:8
Median:6 Q1:6 Q3:8 Mode:6
graphing the data, or counting the quarter and halfway points at 10, 15 and 5, results in Q1 and the median both being 6, while Q3 is 8. 6 is the most common value so it is the mode
Example Question #1 : How To Define Control Groups In An Experiment
A drug company wants to test whether its medication reduces cancer risk. Assuming the company conducts an experiment in which participants are randomly assigned to treatment and control groups, what would the appropriate control group look like?
Those assigned to the control take a sugar pill.
Those assigned to the control take the medication and then suddenly discontinue taking it.
Those assigned to the control take the medication throughout the study period.
Those assigned to the control take a sugar pill.
The only thing you want to vary across groups when you're conducting an experiment is the treatment. Since taking pills is a part of taking medication (the treatment), medical experiments often employ something called a placebo-controlled study where outcomes for those who are randomly assigned to take the medication are compared to outcomes for those who are randomly assigned to take a sugar pill. The sugar pill is expected to have no effect, so it serves as a useful baseline to compare the treatment to.
Example Question #1 : How To Define Control Groups In An Experiment
In a public health study, researchers want to see how the addition of fresh produce stands in inner cities can affect the body weights of people who live within 1 mile of the stands.
The research group gathers data from several groups. Please identify which is the Control group.
Area A received a brand new fresh fruit and vegetable stand.
The researchers gathered information on body weight of people living within 1 mile of this area's central location, both at the starting date and ending date of the study (1 year later).
Area B received a new fresh fruit and vegetable stand.
The researchers gathered information on body weight of people living within 1 mile of this area's central location, both at the starting date and ending date of the study (1 year later).
There is a small town nearby which has several produce stands but also received another new fruit and vegetable stand.
The researchers gathered information on body weight of people living within 1 mile of this area's central location, both at the starting date and ending date of the study (1 year later).
One area of the city received no fresh fruit and vegetable stand.
The researchers gathered information on body weight of people living within 1 mile of this area's central location, both at the starting date and ending date of the study (1 year later).
There is no control group in this study.
One area of the city received no fresh fruit and vegetable stand.
The researchers gathered information on body weight of people living within 1 mile of this area's central location, both at the starting date and ending date of the study (1 year later).
Areas A and B are both experimental areas, where they received the treatment (the new produce stand), so comparing body weights before and after the treatment will provide valuable data.
The area of the city which did not receive the treatment (a produce stand) will provide data of how body weight may change over time naturally, without the stand, in order to compare the effects of the stands elsewhere.
The nearby town already has produce stands and provides residents with a different food environment, so it cannot act as the control group. It has different conditions than the experimental areas A and B, so comparing it to these areas will not provide helpful data in terms of the treatment's effects.
Example Question #1 : How To Define Control Groups In An Experiment
You and your classmate want to test the effect of food coloring on plant color. One of the groups in the experiment receives dye-free water. Which group is this?
Control group
Placebo group
Experimental group
Neither
Control group
The control group receives no treatment.
The experimental group receives the treatment of the independent variable.
Because the flowers getting no dye do not receive the treatment, it is the control group.
Example Question #1 : How To Define Control Groups In An Experiment
You and your friend want to test the effect of different brands of fertilizer on sunflower height.
One group receives no fertilizer during the course of the experiment.
Which group is this?
Experimental group
Control group
Placebo group
Neither
Control group
The control group receives no treatment.
The experimental group receives the treatment of the independent variable.
Because the sunflowers getting no fertilizer do not receive the treatment, it is the control group.
Example Question #1 : How To Define Experimental Units
Of the following examples, which best describes quantitative data?
A student's least favorite sport.
The softness of a chair.
Temperature measurements of water in degrees Fahrenheit.
A child's gender.
College grade level-freshman, sophomore, junior, or senior.
Temperature measurements of water in degrees Fahrenheit.
Quantitative data describes a certain type of information that can be counted or expressed numerically and can be used in meaningful computations. Quantitative data is different from qualitative data, which is primarily involved in describing things in terms of categorizations or specific qualities. Looking at the answer choices, it is clear that measuring the temperature of water in degrees Fahrenheit is a numerical piece of information, and is thus quantitative.
Example Question #1 : How To Define Experimental Units
When designing an experiment, what is the purpose of blocking?
To separate a particular sample into groups previously known to be similar in some way that are expected to affect response to treatments
To hold an extraneous variable constant
To increase the number of experimental units
To use chance to randomly assign experimental units to treatment groups (or vice versa)
None of the other answers
To separate a particular sample into groups previously known to be similar in some way that are expected to affect response to treatments
The purpose of blocking, by definition, is to separate a particular sample into groups previously known to be similar in some way that are expected to affect response to treatments. The other choices pertain to control (keeping an extraneous variable constant), randomization (using random chance to assign experimental units to treatments), and replication (increasing the number of experimental units to reduce chance variation) in an experiment.
Example Question #1 : How To Define Experimental Units
Which of the following is an example of qualitative data?
The amount of carbon monoxide emissions in the air
The average SAT score of students at a particular high school
The temperature of a glass of water
The gender of a high school student
The speed at which a car is traveling
The gender of a high school student
The only example of qualitative data here is the gender of a high school student (i.e. male or female). This cannot be quantified, unlike the other answer choices which all have numbers, quantities, and amounts associated with them.
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