A data set has a mean of 20 and a variance of 16. What is the range of the data

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Question: A data set has a mean of 20 and a variance of 16. What is the range of the data if the maximum value is 28? (2023)

Options:

Correct Answer: 12

Exam Year: 2023

Solution:

If the variance is 16, the standard deviation is 4. The minimum value can be calculated as 20 - 4 = 16. Therefore, range = 28 - 16 = 12.

A data set has a mean of 20 and a variance of 16. What is the range of the data if the maximum value is 28? (2023)

A data set has a mean of 20 and a variance of 16. What is the range of the data if the maximum value is 28? (2023)

Step 1: Understand that the mean of the data set is 20.
Step 2: Know that the variance is 16. The standard deviation is the square root of the variance, so calculate it: sqrt(16) = 4.
Step 3: The standard deviation tells us how much the data values typically differ from the mean. Since the mean is 20 and the standard deviation is 4, we can find the minimum value.
Step 4: Calculate the minimum value by subtracting the standard deviation from the mean: 20 - 4 = 16.
Step 5: We are given that the maximum value in the data set is 28.
Step 6: Now, calculate the range of the data set by subtracting the minimum value from the maximum value: 28 - 16 = 12.

Mean and Variance – Understanding how to calculate the mean and variance of a data set and their implications on the data distribution.
Standard Deviation – Recognizing that the standard deviation is the square root of the variance and how it relates to the data set.
Range Calculation – Calculating the range of a data set using the maximum and minimum values.