Digital PSAT Math Practice Question 208: Answer and Explanation

Question: 208

If a set of 20 different numbers has its smallest and largest values removed, how will that affect the standard deviation of the set?

• A. It will increase.
• B. It will decrease.
• C. It will remain the same.
• D. Not sufficient information.

Correct Answer: B

Explanation:

(B) The smaller the range of values in a data set, the lower the standard deviation will be. If the smallest and largest values are removed, this will decrease the range of values, therefore decreasing the standard deviation.

To be more precise, you can calculate standard deviation using this formula:

For example, the standard deviation of the set {1, 5, 6, 7, 10} is approximately 3.3, while the standard deviation of the same set with the highest and lowest values removed {5, 6, 7} would be 1. So, using this example, you can see that removing the smallest and largest values from the set will decrease the standard deviation of the set.