Question

Both sets of values have an average of 13. Is Set A's standard deviation smaller, larger, or about the same as Set B's? (Note: This question can be answered by knowing the concept of standard deviation, without actually computing the standard deviation). Set A: 1 2 3 23 24 25 Set B: 9 10 11 14 16 18

Answer 1

Hi there!

Set A has a LARGER standard deviation.

A set's standard deviation is equivalent to:

$\sigma = \frac{\sqrt{\Sigma (x - \mu)^2 }}{n-1}$

σ = standard deviation

x = value

μ = mean

n = # of observations

Basically, standard deviation is calculated using how far apart EACH value is from the set's mean. If more values are FARTHER away from the mean, the standard deviation increases and vice-versa.

Set A has a GREATER RANGE and its values are farther from 13 on both sides compared to Set B which has a SMALLER RANGE and its values are closer to 13.

Therefore, Set A will have a larger standard deviation.