Descriptive Statistics
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GMAT Quantitative › Descriptive Statistics
What is the mean of the following data set in terms of 
Explanation
Add the expressions and divide by the number of terms, 8.
The sum of the expressions is:
Divide this by 8:
The average of 10, 25, and 70 is 10 more than the average of 15, 30, and x. What is the missing number?
Explanation
The average of 10, 25, and 70 is 35:
So the average of 15, 30, and the unknown number is 25 or, 10 less than the average of 10, 25, and 70 (= 35)
so
What is the mean of the following data set in terms of
Explanation
Add the expressions and divide by the number of terms, 8.
The sum of the expressions is:
Divide this by 8:
A large group of students is given a standardized test. The following information is given about the scores:
Mean: 73.8
Standard deviation: 6.3
Median: 71
25th percentile: 61
75th percentile: 86
Highest score: 100
Lowest score: 12
What is the interquartile range of the tests?
More information about the scores is needed.
Explanation
The interquartile range of a data set is the difference between the 75th and 25th percentiles:
All other given information is extraneous to the problem.
The average of 10, 25, and 70 is 10 more than the average of 15, 30, and x. What is the missing number?
Explanation
The average of 10, 25, and 70 is 35:
So the average of 15, 30, and the unknown number is 25 or, 10 less than the average of 10, 25, and 70 (= 35)
so
What is the median of the following numbers?
Explanation
The median of a data set with an even number of elements is the mean of its two middle elements, when ranked. The set is already ranked, so just find the mean of middle elements 
Give the median of the following data set in terms of 
Explanation
The data set can be arranged from least to greatest as follows:
The median of a data set with eight elements is the mean of its fourth-highest and fourth-lowest elements, which are 
Below is the stem-and-leaf display of a set of test scores.
What is the interquartile range of these test scores?
Explanation
The numbers in the "stem" of this display represent tens digits of the test scores, and the numbers in the "leaves" represent the units digits. This stem-and-leaf display represents twenty scores.
The interquartile range is the difference of the third and first quartiles.
The third quartile is the median of the upper half, or the upper ten scores. This is the arithmetic mean of the fifth- and sixth-highest scores. These scores are 73 and 69, so the mean is 
The first quartile is the median of the lower half, or the lower ten scores. This is the arithmetic mean of the fifth- and sixth-lowest scores. Both of these scores are the same, however - 57.
The interquartile range is therefore the difference of these numbers:
What is the mean of this data set?
Explanation
Add the numbers and divide by 6:
Below is the stem-and-leaf display of a set of test scores.
What is the first quartile of these test scores?
Explanation
The numbers in the "stem" of this display represent tens digits of the test scores, and the numbers in the "leaves" represent the units digits.
This stem-and-leaf display represents twenty scores. The first quartile is the median of the lower half, or the lower ten scores. This is the arithmetic mean of the fifth- and sixth-lowest scores. Both of these scores are the same, however - 57. Therefore, 57 is the first quartile.