Question

Which of the following sets of numbers has the largest standard deviation? (No calculations are required.)

A) {4,5,6,7}
B){12,13,14,15}
C){18,18,18,18}
D) {1,2,9,10}

Answer 1

Set D) {1,2,9,10} has the largest standard deviation because it has the greatest spread of values, with some at one extreme and others at the opposite extreme, illustrating more variability compared to the other sets.

Step-by-step explanation:

The question asks which set of numbers has the largest standard deviation. Standard deviation represents the amount of variation or dispersion of a set of values. A set with a larger standard deviation has values that are more spread out from the mean, whereas a set with a small standard deviation has values that are closer to the mean. Comparing the given sets:

• A) {4,5,6,7}
• B) {12,13,14,15}
• C) {18,18,18,18}
• D) {1,2,9,10}

Set A and B have values that are evenly spread and will have a standard deviation that is not very large. Set C has no spread at all; all values are the same, which means the standard deviation is 0. Set D, however, has a greater spread with values 1, 2 at one extreme and values 9, 10 at the other. Thus, even without performing calculations, we can conclude that set D) {1,2,9,10} has the largest standard deviation.