Which of the following sets of four numbers has the smallest standard deviation?
A)7, 8, 9, 10
B)5, 5, 5, 6
C)0, 0, 10, 10
D)0, 1, 2, 3

Question

Quizplus · Accepted Answer

To determine which set has the smallest standard deviation, we need to calculate the standard deviation of each set. The formula for the standard deviation of a set of numbers is:

SD = sqrt((sum of (value - mean)^2) / number of values)

Using this formula, we can calculate the standard deviation of each set:
A) Mean = 8.5, SD = 1.12
B) Mean = 5.25, SD = 0.43
C) Mean = 5, SD = 5
D) Mean = 1.5, SD = 1.12

Since B has the smallest standard deviation, the answer is B. This is because all the values are relatively close to the mean, which means there is less variation in the set. Sets A and D have larger standard deviations because the values are further from the mean. Set C has a large standard deviation because it contains both 0 and 10, which are very different from each other and the mean.

Which of the Following Sets of Four Numbers Has the Smallest