Question

Here are the prices of five new bicycles, in dollars: 25, 30, 50, 77, 80.

The standard deviation is about $26.

If a sixth bike is added to the sample that has a price of $400, what happens to the standard deviation?

A. The new standard deviation is less than $26.
B. The new standard deviation is greater than $26.
C. The new standard deviation is $426.
D. The standard deviation is still $26.

Answer 1

B. The new standard deviation is greater than $26.

Explanation:

Answer 2

The new standard deviation is greater than $26.

Explanation:

The 6th bicycle would bring a number way out of the range of the prices of the first 5 bicycle.

That would more than double the mean (form 52 to 110) and the standard variance will jump from 26 to 144!

Don't forget that the standard deviation indicates how spread out the numbers of the sample are. Since you introduce a number that is WAY out of the range of the other values, it's normal for it to affect the standard deviation a lot!