CLEP College Mathematics: Descriptive Statistics Practice Questions
Compare centers and spreads with eight original data problems. Compute means, medians and ranges, then reason about outliers, constant shifts and the width of a normal distribution.
Free original practice questions for study purposes. Open Exam Prep is an independent study resource and is not affiliated with, endorsed by, or sponsored by the makers of CLEP.
Answer the questions below — you get instant feedback and a full explanation for each.
1. The values in a data set are 4, 7, 7, 10 and 12. What is their arithmetic mean?
Explanation. Add all five values: 4 + 7 + 7 + 10 + 12 = 40. Divide by the number of values: 40/5 = 8. The repeated 7 counts twice.
2. The sorted data set is 2, 4, 6, 8, 11, 19. What is its median?
Explanation. There are six values, so the median is the average of the third and fourth: (6 + 8)/2 = 7. It is not necessary for the median to be an observed value.
3. Three quiz scores are 70 points each and two are 90 points each. What is the mean of all five scores?
Explanation. The total is 3(70) + 2(90) = 390 points across 5 scores. The mean is 390/5 = 78. Averaging 70 and 90 directly would incorrectly give the two groups equal weight.
4. What is the range of the data set -4, 3, 8, 12?
Explanation. Range is the largest value minus the smallest: 12 - (-4) = 16. Subtracting a negative increases the difference.
5. In the data set 1, 4, 6, 9, 20, the value 20 is replaced by 100. What happens to the mean and median?
Explanation. The total increases by 100 - 20 = 80 across five values, so the mean increases by 80/5 = 16. The middle value remains 6, so the median is unchanged.
6. Five observations have a mean of 6. Four of them are 2, 4, 7 and 9. What is the fifth observation?
Explanation. The required total is 5 times 6 = 30. The four known observations sum to 2 + 4 + 7 + 9 = 22. The missing observation is 30 - 22 = 8.
7. A new data set is formed by adding 5 to every value in a data set containing at least two values. Using the same definition of standard deviation before and after, what happens?
Explanation. The center shifts by 5. Each deviation from the mean stays the same because (x + 5) - (mean + 5) = x - mean. Squared deviations and thus standard deviation remain unchanged.
8. Populations A and B are normally distributed with mean 100. Their standard deviations are 10 and 20, respectively. Which population has the larger proportion of values between 90 and 110?
Explanation. For A, the interval runs from one standard deviation below the mean to one above. For B, it runs from half a standard deviation below to half above. A normal distribution places more probability within the wider standardized interval, so A has the larger proportion.
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FAQ
Why can a weighted mean differ from the average of two group means?
A larger group contributes more observations. Multiply each group mean by its size and divide the combined total by the combined size.
Which center is less sensitive to an extreme value?
The median usually changes less because it depends on ordered position. The mean depends on every numerical value.
Do I need lengthy standard-deviation calculations for this set?
No. The spread questions use conceptual comparisons, matching the conceptual treatment specified in the CLEP College Mathematics outline.