A data set has a mean of 50 and a variance of 25. What is the standard deviation

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Question: A data set has a mean of 50 and a variance of 25. What is the standard deviation? (2021)

Options:

Correct Answer: 10

Exam Year: 2021

Solution:

Standard deviation is the square root of variance. Therefore, SD = √25 = 5.

A data set has a mean of 50 and a variance of 25. What is the standard deviation? (2021)

A data set has a mean of 50 and a variance of 25. What is the standard deviation? (2021)

Step 1: Understand that variance is a measure of how spread out the numbers in a data set are.
Step 2: Know that the standard deviation is a value that tells us how much the numbers in the data set typically differ from the mean.
Step 3: Remember that the standard deviation is calculated by taking the square root of the variance.
Step 4: Since the variance given in the question is 25, we need to find the square root of 25.
Step 5: Calculate the square root of 25, which is 5.
Step 6: Conclude that the standard deviation is 5.

Mean and Variance – Understanding the mean as the average of a data set and variance as a measure of data spread.
Standard Deviation – The standard deviation is the square root of the variance, indicating how much individual data points deviate from the mean.