The table above shows two lists of numbers. Which of the following is a true statement comparing list A and list B ?

Options

A. The means are the same, and the standard deviations are different.
B. The means are the same, and the standard deviations are the same.
C. The means are different, and the standard deviations are different.
D. The means are different, and the standard deviations are the same.

Answer

A

Explanation

The mean number of each list is found by dividing the sum of all the numbers in each list by the count of the numbers in each list. The mean of list A is `(1+2+3+4+5+6)/6`=3.5 , and the mean of list B is `(2+3+3+4+4+5)/6=3.5` Thus, the means are the same. The standard deviations can be compared by inspecting the distances of the numbers in each list from the mean. List A contains two numbers that are 0.5 from the mean, two numbers that are 1.5 from the mean, and two numbers that are 2.5 from the mean. List B contains four numbers that are 0.5 from the mean and two numbers that are 1.5 from the mean. Overall, list B contains numbers that are closer to the mean than are the numbers in list A, so the standard deviations of the lists are different.
Choice B is incorrect and may result from assuming that two data sets with the same mean must also have the same standard deviation. Choices C and D are incorrect and may result from an error in calculating the means.