PSAT Math Multiple-Choice Question 755: Answer and Explanation

Question: 755

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. The standard deviation will increase.
• B. The standard deviation will decrease.
• C. The standard deviation will remain the same.
• D. Not enough information is provided.

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, the range of values will decrease, thereby 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. The standard deviation of the same set with the highest and lowest values removed {5, 6, 7} is 1. By using this example, you can see that removing the smallest and largest values from the set decreases the standard deviation of the set.