The maximum value of a data set consisting of 25 positive integers is 84. A new data set consisting of 26 positive integers is created by including 96 in the original data set. Which of the following measures must be 12 greater for the new data set than for the original data set?

Options

A. The mean
B. The median
C. The range
D. The standard deviation

Answer

C

Explanation

Let m be the minimum value of the original data set. The range of a data set is the difference between the maximum value and the minimum value. The range of the original data set is therefore 84 − m. The new data set consists of the original set and the positive integer 96. Thus, the new data set has the same minimum m and a maximum of 96. Therefore, the range of the new data set is 96 − m. The difference in the two ranges can be found by subtracting the ranges: (96 − m) − (84 − m). Using the distributive property, this can be rewritten as 96 − m − 84 + m, which is equal to 12. Therefore, the range of the new data set must be 12 greater than the range of the original data set.
Choices A, B, and D are incorrect. Only the maximum value of the original data set is known, so the amount that the mean, median, and standard deviation of the new data set differ from those of the original data set can’t be determined.