If the mean of a data set is 50 and the variance is 25, what is the standard dev

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Question: If the mean of a data set is 50 and the variance is 25, what is the standard deviation? (2019)

Options:

Correct Answer: 10

Exam Year: 2019

Solution:

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

If the mean of a data set is 50 and the variance is 25, what is the standard deviation? (2019)

If the mean of a data set is 50 and the variance is 25, what is the standard deviation? (2019)

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 the formula that relates standard deviation (SD) to variance: SD = √(variance).
Step 4: Since the variance given in the question is 25, substitute this value into the formula: SD = √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 relationship between mean, variance, and standard deviation in a data set.
Standard Deviation Calculation – Knowing that standard deviation is the square root of variance.