20 easy SAT One-variable data: center & spread questions
These are the questions most test-takers get right. They are worth practising anyway: on the digital SAT the easy questions in Module 1 are what route you into the harder, higher-scoring Module 2, so dropping one costs more than it looks.
Every question below is a real item from the SAT Climb bank, tagged easy by the same difficulty model the app uses to build your practice. Pick an answer before you open the explanation.
Math · Problem-Solving and Data Analysis~2 per testEasy tier
25, 28, 30, 30, 32, 35, 40 What is the mean of the data set shown?
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Why B is right
The mean is the sum of all values divided by the number of values. The sum is 25 + 28 + 30 + 30 + 32 + 35 + 40 = 220, and there are 7 values, so the mean is 220 ÷ 7, which rounds to 31.43.
Why the others are wrong
AThis is the median of the data set (the middle value), not the mean.
CThis incorrectly rounds the mean down or uses an incorrect calculation method.
DThis incorrectly calculates a weighted value or excludes the outlier 40 from the calculation.
Question 2Easy
Number Frequency
8 3
11 5
14 2
The table shows the frequency distribution for a data set. What is the mean of this data set?
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Why B is right
The mean is the sum of all values divided by the total frequency. The sum is (8 × 3) + (11 × 5) + (14 × 2) = 24 + 55 + 28 = 107. The total frequency is 3 + 5 + 2 = 10. The mean is 107 ÷ 10 = 10.7.
Why the others are wrong
AThis is the median of the expanded data set, not the mean.
CThis incorrectly divides the sum of the distinct values (8 + 11 + 14 = 33) by 3, ignoring the frequencies.
DThis incorrectly uses only the most frequent value (11) and adds 1, ignoring proper weighted calculation.
Question 3Easy
A data set consists of the following values: 2, 4, 6, 6, 8, 10. If the value 20 is added to this data set, how does the median change?
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Why B is right
The original median is 6 (average of 6 and 6, the 3rd and 4th values). After adding 20, the new data set has 7 values: 2, 4, 6, 6, 8, 10, 20, and the median is still 6 (the 4th value). The median does not change.
Why the others are wrong
AThis incorrectly assumes the median changes proportionally with the mean.
CThis incorrectly assumes the median shifts to 7 by averaging different values.
DThis confuses the effect on the median with the effect on other measures like the range.
Question 4Easy
Data set R: 40, 45, 50, 55, 60
Data set S: 49, 50, 50, 50, 51
Which data set has the greater standard deviation?
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Why D is right
Data set R has values spread evenly across a range of 20 (from 40 to 60), while data set S has values clustered very tightly around 50 with a range of only 2 (from 49 to 51). Data set R has the greater standard deviation due to its much greater spread.
Why the others are wrong
AThe spreads are clearly different, with data set R showing much more dispersion than data set S.
BData set S has minimal variation with most values at 50, resulting in much smaller standard deviation than data set R.
CThe difference in spread is clearly observable from the given values.
Question 5Easy
A data set consists of 9 values with a median of 18. If the smallest value is removed, which of the following must be true about the new data set?
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Why C is right
With 9 values, the median is the 5th value (18). Removing the smallest value leaves 8 values, so the new median is the average of the 4th and 5th values in the original list. Since the 5th value is 18 and values are ordered, the new median must be at least 18.
Why the others are wrong
AThis incorrectly assumes the median never changes when a value is removed.
BThis incorrectly assumes the median must strictly increase, but it could stay at 18.
DThis confuses mean and median, and provides no basis for this claim.
Question 6Easy
1, 3, 3, 5, 7, 7, 7, 9, 20. What is the mean of this data set?
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Why A is right
The mean is the sum of all values divided by the number of values. The sum is 1 + 3 + 3 + 5 + 7 + 7 + 7 + 9 + 20 = 62, and there are 9 values, so the mean is 62/9, which equals approximately 6.89.
Why the others are wrong
BThis is the median of the data set, not the mean.
CThis incorrectly excludes the outlier value 20 from the calculation.
DThis incorrectly uses 10 values instead of 9 in the denominator.
Question 7Easy
Number | Frequency
2 | 3
4 | 5
6 | 2
8 | 2
The frequency table shown represents a data set. What is the median of this data set?
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Why A is right
The total frequency is 3 + 5 + 2 + 2 = 12. The data set in order is: 2, 2, 2, 4, 4, 4, 4, 4, 6, 6, 8, 8. The median is the average of the 6th and 7th values, which are both 4, so the median is 4.
Why the others are wrong
BThis is approximately the mean of the data set, not the median.
CThis incorrectly takes the middle value from the frequency table rows rather than the actual data values.
DThis incorrectly identifies the 7th value as 6 by miscounting positions in the ordered list.
Question 8Easy
5, 8, 8, 10, 12, 15, 20 If the value 20 is removed from the data set shown, what is the effect on the median?
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Why A is right
The original median is the fourth value in the seven-value set: 10. After removing 20, the new median is the average of the third and fourth values: (8 + 10) ÷ 2 = 9. The median decreases by 1.
Why the others are wrong
BThis incorrectly calculates the change by comparing the original median to 8 instead of to the new median of 9.
CRemoving the maximum value affects the median when the data set has an odd number of values.
DRemoving the largest value decreases the median, not increases it.
Question 9Easy
Data set X: 10, 10, 10, 10, 10
Data set Y: 8, 9, 10, 11, 12
Which data set has the greater standard deviation?
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Why B is right
Data set X has all identical values, so every value equals the mean and the standard deviation is zero. Data set Y has values that vary from the mean, so it has a positive standard deviation. Therefore, data set Y has the greater standard deviation.
Why the others are wrong
AData set X has zero variation since all values are identical, resulting in zero standard deviation.
CData set X has zero standard deviation while data set Y has positive standard deviation due to variation in its values.
DThe spreads are clearly different and can be qualitatively compared.
Question 10Easy
A data set consists of the following values: 14, 16, 18, 18, 19, 21. What is the mean of this data set?
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Why D is right
The mean is the sum of the values divided by the number of values. The sum is 14 + 16 + 18 + 18 + 19 + 21 = 106. The mean is 106 ÷ 6, which equals 17.67 (rounded to two decimal places).
Why the others are wrong
AThis is the median of the data set, not the mean.
BThis incorrectly rounds down from the correct mean.
CThis incorrectly selects one of the larger values without calculating the mean.
Question 11Easy
The following frequency table shows the number of books read by students in a month. Number of Books: 2 (Frequency: 3), 4 (Frequency: 5), 6 (Frequency: 2). What is the median number of books read?
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Why B is right
There are 10 total values (3+5+2). The ordered list is 2, 2, 2, 4, 4, 4, 4, 4, 6, 6. With 10 values, the median is the average of the 5th and 6th values, which are both 4, so the median is 4.
Why the others are wrong
AThis is the mean, calculated as (2×3 + 4×5 + 6×2)/10, not the median.
CThis incorrectly treats the frequency values themselves as data, averaging 3, 5, and 2.
DThis incorrectly identifies the maximum value as the median.
Question 12Easy
A data set has 5 values: 3, 7, 7, 9, 14. If the value 14 is removed from this data set, which of the following quantities will decrease?
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Why C is right
The original mean is (3 + 7 + 7 + 9 + 14) / 5 = 40 / 5 = 8. After removing 14, the mean is (3 + 7 + 7 + 9) / 4 = 26 / 4 = 6.5, which decreases. The original median is 7 (the middle value), and after removing 14, the median remains 7 (the average of the two middle values 7 and 7). The original range is 14 - 3 = 11, and after removing 14, the range is 9 - 3 = 6, which decreases. Therefore, the mean and the range decrease.
Why the others are wrong
AThis choice incorrectly suggests that only the median decreases. The median remains 7 both before and after removing 14, so it does not change.
BThis choice incorrectly suggests that only the mean decreases. While the mean does decrease, the range also decreases when 14 is removed.
DThis choice incorrectly includes the median as a quantity that decreases. The median is 7 in the original set and remains 7 after removing 14, so it does not change.
Question 13Easy
Data set V: 12, 14, 16, 18, 20, 22, 24
Data set W: 17, 17, 18, 18, 19, 19, 19
Which data set has the greater standard deviation?
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Why D is right
Data set V spans from 12 to 24 (range of 12) with values evenly distributed, while data set W spans from 17 to 19 (range of 2) with values tightly clustered. The much greater spread in data set V means it has the greater standard deviation.
Why the others are wrong
AData set W has values clustered in a narrow range, resulting in less variation than data set V.
BThe spreads are clearly different and can be compared by observing the dispersion of values.
CThe two data sets have distinctly different spreads, with data set V showing much more variation.
Question 14Easy
4, 6, 6, 8, 10, 12, 12. What is the mean of this data set?
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Why D is right
The mean is the sum of all values divided by the number of values. The sum is 4 + 6 + 6 + 8 + 10 + 12 + 12 = 58, and there are 7 values, so the mean is 58/7, which equals approximately 8.29.
Why the others are wrong
AThis incorrectly computes the mean using only 6 values instead of 7.
BThis is the median of the data set, not the mean.
CThis incorrectly rounds or estimates the mean.
Question 15Easy
Number: 2, 5, 8, 11. Frequency: 3, 4, 2, 1. What is the median of the data represented in this frequency table?
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Why B is right
The frequency table represents 10 data values: 2, 2, 2, 5, 5, 5, 5, 8, 8, 11. The median of 10 values is the average of the 5th and 6th values, which are both 5, so the median is 5.
Why the others are wrong
AThis is close to the mean of the data set, not the median.
CThis incorrectly averages values that are not in the middle positions.
DThis incorrectly identifies a middle position without accounting for the frequency distribution.
Question 16Easy
9, 10, 11, 11, 11, 13, 14. A value of 11 is added to this data set. How does the median change?
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Why C is right
The original data set has 7 values, and the median is the 4th value, which is 11. After adding another 11, the data set becomes 9, 10, 11, 11, 11, 11, 13, 14 (8 values), and the median is the average of the 4th and 5th values: (11 + 11) / 2 = 11. The median remains 11.
Why the others are wrong
AThis incorrectly assumes the median shifts to an intermediate value when transitioning from odd to even count.
BThis applies the change in mean (which slightly decreases) to the median instead.
DThis incorrectly assumes that adding a value equal to the median shifts the median upward.
Question 17Easy
Data set A: 2, 4, 6, 8, 10
Data set B: 5, 5, 6, 7, 7
Which data set has the greater standard deviation?
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Why A is right
Data set A spans from 2 to 10 (range of 8), while data set B spans from 5 to 7 (range of 2). The values in data set A are much more spread out from the mean, so data set A has the greater standard deviation.
Why the others are wrong
BThis incorrectly identifies the data set with less spread as having greater standard deviation.
CThe two data sets have clearly different spreads, with data set A's values much more dispersed than data set B's clustered values.
DStandard deviation can be qualitatively compared by observing the spread of values without computing exact values.
Question 18Easy
Data set M: 15, 20, 25, 30, 35
Data set N: 24, 25, 25, 25, 26
Which data set has the greater standard deviation?
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Why C is right
Data set M has values spread across a range of 20 (from 15 to 35), while data set N has values clustered tightly around 25 with a range of only 2 (from 24 to 26). The much greater spread in data set M means it has the greater standard deviation.
Why the others are wrong
AData set N has values tightly clustered near 25, indicating much less variation than data set M.
BThe spreads are clearly different, with data set M showing much greater dispersion.
DThe difference in spread between the two data sets is evident from inspection.
Question 19Easy
Data set P: 3, 6, 9, 12, 15, 18
Data set Q: 10, 10, 11, 11, 12, 12
Which data set has the greater standard deviation?
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Why A is right
Data set P spans from 3 to 18 (range of 15) with values evenly spread, while data set Q spans from 10 to 12 (range of 2) with values tightly clustered. The greater spread in data set P results in greater standard deviation.
Why the others are wrong
BData set Q has much less spread than data set P, so it has the smaller standard deviation.
CThe two data sets have clearly different spreads, with data set P showing much more variation.
DThe spreads can be qualitatively compared by observing the range and dispersion of values.
Question 20Easy
Data set T: 1, 5, 5, 5, 9
Data set U: 4, 5, 5, 5, 6
Which data set has the greater standard deviation?
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Why C is right
Data set T has values ranging from 1 to 9 (range of 8) with extreme values far from the mean, while data set U ranges from 4 to 6 (range of 2) with values close to the mean. Data set T has the greater standard deviation.
Why the others are wrong
AData set U has a much smaller range and less dispersion than data set T.
BThe spreads differ significantly, with data set T showing much more variation from the mean.
DThe relative spreads are clearly discernible from the given data.
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