SAT Data Analysis: Master Every Question Type
Read the data.
Beat the question.
40 original SAT-style questions designed to take you from basic statistical skills to the questions where the real challenge is deciding what the data actually tell you.
How to use this page
Don’t rush through the answer choices. For every question, first identify what information is actually given. Then decide which statistical idea applies.
The first 24 questions build the core toolkit. The final 16 questions deliberately become more conceptual and test your ability to reason from statistical information.
The SAT Data Mindset
Mean
Find the average—and use the average to work backward.
A teacher records the numbers of minutes that 5 students spent completing a practice assignment:
\[ 42,\quad35,\quad38,\quad45,\quad40 \]
What is the mean number of minutes?
Add the values:
There are 5 values, so:
The mean of the five numbers
\[ 18,\quad24,\quad27,\quad31,\quad x \]
is 26. What is the value of \(x\)?
If the mean is 26 and there are 5 values, the total must be:
The known values total:
Therefore:
Median
Find the middle—but only after putting the data in order.
The numbers below represent the number of books read by 7 students during the summer:
\[ 3,\quad8,\quad5,\quad11,\quad6,\quad4,\quad9 \]
What is the median?
Step 1 — Sort the data.
Step 2 — Find the middle value.
There are 7 values, so the median is the 4th value:
The five numbers below are arranged in increasing order:
\[ 12,\quad18,\quad x,\quad27,\quad35 \]
The median is 23. What is \(x\)?
There are five ordered values, so the median is the third value.
Range
Measure the distance from the minimum to the maximum.
The daily high temperatures, in degrees Fahrenheit, during a five-day period were:
\[ 71,\quad76,\quad68,\quad80,\quad74 \]
What was the range?
The maximum is \(80\), and the minimum is \(68\).
The numbers of visitors to two museums over five days are shown below.
| Museum A | Museum B |
|---|---|
| 120, 135, 140, 150, 155 | 105, 125, 140, 160, 180 |
How much greater is the range for Museum B than the range for Museum A?
For Museum A:
For Museum B:
Difference:
Percentiles
Understand where a value stands relative to a group.
A student scored at the 82nd percentile on a mathematics assessment. Which statement is the best interpretation?
A percentile describes a student’s relative position compared with other scores.
Student A scored at the 74th percentile on a test, while Student B scored at the 91st percentile.
Which statement must be true?
A percentile tells us about relative standing. The 91st-percentile student had a higher position within the comparison group.
Quartiles & IQR (Interquartile Range)
Measure the spread of the middle 50% of the data.
Consider the ordered data set:
The first quartile is \(Q_1=7\), and the third quartile is \(Q_3=21\). What is the interquartile range?
Two groups have the following quartiles:
| Group | \(Q_1\) | \(Q_3\) |
|---|---|---|
| A | 18 | 30 |
| B | 12 | 32 |
Which group has the greater interquartile range?
Group A:
Group B:
Therefore, Group B has the greater IQR.
Box Plots
Read the five-number summary directly from a visual.
The box plot above represents the distribution of the number of minutes that students spent exercising each day.
The five-number summary is:
What is the median?
The median is represented by the line inside the box.
Two box plots represent the distributions of monthly transportation costs for two groups of students.
| Group | \(Q_1\) | \(Q_3\) |
|---|---|---|
| A | 40 | 70 |
| B | 35 | 80 |
Which group has the greater interquartile range?
Therefore, Group B has the greater IQR.
Histograms
Read grouped numerical data and interpret frequency.
A histogram shows the number of students who spent the following amounts of time studying for a test.
| Study time (hours) | Number of students |
|---|---|
| 0–2 | 4 |
| 2–4 | 9 |
| 4–6 | 12 |
| 6–8 | 7 |
| 8–10 | 3 |
How many students studied between 4 and 6 hours?
The interval from 4 to 6 hours has a frequency of 12.
The histogram below represents the commute times, in minutes, of employees at a company.
| Commute time | Frequency |
|---|---|
| 0–10 | 5 |
| 10–20 | 14 |
| 20–30 | 18 |
| 30–40 | 11 |
| 40–50 | 4 |
How many more employees have commute times between 20 and 30 minutes than between 40 and 50 minutes?
Dot Plots
Every dot represents an individual observation.
A dot plot represents the number of goals scored by a soccer team in 9 games:
What is the median number of goals?
There are 9 observations, so the median is the 5th value.
Class A
Class B
Which statement is true?
Therefore, Class B has the greater range.
Frequency Tables
Use frequency to organize repeated observations.
The table shows the number of books read by students during a month.
| Books read | Frequency |
|---|---|
| 1 | 2 |
| 2 | 5 |
| 3 | 6 |
| 4 | 3 |
What is the mean number of books read?
Multiply each value by its frequency:
Total books:
Total students:
Therefore:
The table shows the number of pets owned by students.
| Number of pets | Number of students |
|---|---|
| 0 | 4 |
| 1 | 7 |
| 2 | \(x\) |
| 3 | 3 |
There are 20 students in total. What is \(x\)?
Scatterplots & Association
Recognize direction and strength before doing any arithmetic.
A researcher creates a scatterplot comparing the number of hours students spend studying with their scores on a mathematics assessment. The points generally rise from left to right.
Which statement best describes the association?
As study time increases, assessment scores generally increase. Therefore, the variables have a positive association.
Two scatterplots show the relationship between \(x\) and \(y\).
- Plot A: The points lie very close to a downward-sloping line.
- Plot B: The points generally slope downward but are widely scattered.
Which statement is true?
Both plots have a downward trend, so both have negative associations. However, Plot A’s points are much closer to a clear line.
Therefore, Plot A has the stronger negative association.
Line of Best Fit
Use a model to make predictions and interpret slope in context.
A line of best fit for a data set relating the number of hours a student studies, \(x\), to the student’s test score, \(y\), is
What does the slope of 6.5 represent?
The slope tells us how much \(y\) changes for a 1-unit increase in \(x\).
Here, \(x\) represents hours studied and \(y\) represents test score. Therefore, an additional hour corresponds to a predicted increase of 6.5 points.
The line of best fit for the relationship between the age of a car, \(x\), in years and its value, \(y\), in thousands of dollars is
According to the model, what is the predicted value of a 5-year-old car?
A 5-year-old car means \(x=5\).
Because \(y\) is measured in thousands of dollars:
Two-Way Tables & Relative Frequency
Compare groups carefully—especially the denominator.
| Activity | No Activity | Total | |
|---|---|---|---|
| Freshmen | 48 | 32 | 80 |
| Sophomores | 54 | 26 | 80 |
| Juniors | 24 | 16 | 40 |
| Total | 126 | 74 | 200 |
What percentage of the surveyed juniors participate in an after-school activity?
The question asks about juniors, so the denominator is the total number of juniors:
Of those 40 students, 24 participate.
| Morning | Evening | Total | |
|---|---|---|---|
| Grade 11 | 72 | 48 | 120 |
| Grade 12 | 81 | 99 | 180 |
Which statement is true?
Grade 11:
Grade 12:
Therefore, a greater percentage of Grade 11 students prefer morning study.
Calculate less. Reason more.
Before choosing an answer, ask yourself: What is guaranteed by the information given?
Standard Deviation
Understand spread around the mean.
Two neighborhoods have the same mean home price.
| Mean | Standard Deviation | |
|---|---|---|
| Neighborhood A | \$400,000 | \$15,000 |
| Neighborhood B | \$400,000 | \$60,000 |
Which statement is best supported by the information?
Both neighborhoods have the same mean:
But Neighborhood A has the smaller standard deviation:
A smaller standard deviation indicates that the values tend to be less spread out around the mean.
Two classes receive scores on the same assessment.
| Class | Mean | Standard Deviation |
|---|---|---|
| A | 80 | 3 |
| B | 80 | 9 |
Which statement must be true?
The means are identical, but:
Therefore, Class A’s scores have less variability around the mean.
Comparing Distributions
Read center and spread together.
The distributions of delivery times for two restaurants are summarized below.
| Restaurant | Mean | Standard Deviation |
|---|---|---|
| A | 32 min | 4 min |
| B | 32 min | 11 min |
Which statement is best supported?
Both means are 32 minutes. Restaurant A has the smaller standard deviation:
Therefore, Restaurant A’s delivery times tend to be less spread out and more consistent.
| Group | Mean | Standard Deviation |
|---|---|---|
| X | 68 | 5 |
| Y | 82 | 5 |
Which statement is best supported?
The standard deviations are both:
Therefore, the two groups have the same measured amount of spread according to standard deviation.
Transforming a Data Set
What changes when the same number is added to every value?
Every value moves by the same amount, so the distances between the values remain unchanged.
The mean of a data set is 48 and the standard deviation is 6. A new data set is created by adding 10 to every value.
What are the mean and standard deviation of the new data set?
Adding 10 to every value shifts the entire distribution by 10.
But the distances between the data values do not change, so the standard deviation remains 6.
A data set has:
- mean = 72
- median = 70
- range = 24
- standard deviation = 5
A new data set is created by subtracting 8 from every value. Which quantity remains unchanged?
Subtracting 8 from every value shifts the distribution but does not change the distances between values.
Therefore, the range remains unchanged.
Scaling a Data Set
Multiplying every value stretches the distribution.
The mean of a data set is 15, and its standard deviation is 4. Every value in the data set is multiplied by 3.
What are the new mean and standard deviation?
The mean is multiplied by 3:
The standard deviation is also multiplied by 3:
A data set has a range of 18. A new data set is created by multiplying every value by 5.
What is the range of the new data set?
Multiplying every value by 5 multiplies the distance between the minimum and maximum by 5.
Outliers & Their Impact
One unusual value can dramatically change some statistics.
A data set contains the following home prices, in thousands of dollars:
A home priced at \$1,500,000 is added to the data set. Which statistic is most likely to increase substantially?
The new value is extremely large compared with the other values. The mean uses every value, so an extreme value can pull the mean substantially upward.
The median is much less affected by a single extreme value.
A researcher records the following annual incomes, in thousands of dollars:
Which measure of center would generally be more representative of the income of a typical person in this group?
The value 500 is an extreme outlier. Because the mean uses every value, the \$500,000 income pulls the mean upward.
The median is much less affected by the extreme value.
What Must Be True?
Separate guaranteed conclusions from merely possible ones.
| Group A | Group B | |
|---|---|---|
| Mean | 75 | 75 |
| Standard deviation | 4 | 10 |
Which statement must be true?
Both groups have the same mean:
But:
Therefore, Group A has less variability around the mean.
A data set has a mean of 52 and a range of 18. A new data set is created by adding 7 to every value.
Which statement must be true?
Adding 7 to every value shifts the entire distribution by 7.
But the range measures the distance between the minimum and maximum. Both values increase by 7, so their difference remains unchanged:
What Can Be Inferred?
Don’t claim more than the data actually support.
A data set has a mean of 100 and a standard deviation of 12. Which statement is best supported?
Standard deviation describes the amount of variability around the mean. It does not tell us the exact minimum or maximum.
Therefore, we cannot conclude that all values lie between \(88\) and \(112\).
| Group A | Group B | |
|---|---|---|
| Mean | 78 | 84 |
| Median | 80 | 83 |
| Standard deviation | 5 | 5 |
Which statement can be inferred from the table?
The table directly gives:
Since:
Group B had a higher mean score.
Real-World Statistical Reasoning
The final challenge: combine several statistical ideas.
Two neighborhoods have the following statistics for home prices.
| Neighborhood A | Neighborhood B | |
|---|---|---|
| Mean price | \$420,000 | \$420,000 |
| Median price | \$415,000 | \$410,000 |
| Standard deviation | \$18,000 | \$52,000 |
Which statement is best supported?
The two neighborhoods have the same mean:
But:
Therefore, Neighborhood A has a smaller standard deviation and less variability around the mean.
A researcher compares the weekly exercise times of two groups.
| Group X | Group Y | |
|---|---|---|
| Mean | 150 min | 150 min |
| Median | 148 min | 149 min |
| Standard deviation | 12 min | 30 min |
The researcher then adds 20 minutes to every observation in both groups.
Which statement is true about the resulting data sets?
Adding 20 minutes to every observation shifts each distribution by 20 minutes.
For both groups:
So both means increase by 20 minutes.
However, the distance between observations does not change. Therefore, the standard deviations remain:
Mean changes. Median changes. Range stays the same. Standard deviation stays the same.
Data Detective Complete.
You’ve gone from calculating basic statistics to reasoning about what distributions, standard deviations, transformations, and real-world data actually tell you.