If the mean of a data set is 50 and the standard deviation is 10, what is the va

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Question: If the mean of a data set is 50 and the standard deviation is 10, what is the variance? (2023)

Options:

Correct Answer: 100

Exam Year: 2023

Solution:

Variance is the square of the standard deviation. Therefore, variance = 10² = 100.

If the mean of a data set is 50 and the standard deviation is 10, what is the variance? (2023)

If the mean of a data set is 50 and the standard deviation is 10, what is the variance? (2023)

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 variance is calculated by squaring the standard deviation.
Step 4: Since the standard deviation given is 10, we will square this value.
Step 5: Calculate 10 squared, which is 10 * 10 = 100.
Step 6: Conclude that the variance of the data set is 100.

Mean and Standard Deviation – Understanding the relationship between mean, standard deviation, and variance in a data set.
Variance Calculation – Knowing that variance is calculated as the square of the standard deviation.