If the data set is: 5, 5, 5, 5, what is the variance? (2019)

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Question: If the data set is: 5, 5, 5, 5, what is the variance? (2019)

Options:

Correct Answer: 0

Exam Year: 2019

Solution:

All values are the same, so variance = 0.

If the data set is: 5, 5, 5, 5, what is the variance? (2019)

If the data set is: 5, 5, 5, 5, what is the variance? (2019)

Step 1: Identify the data set. The data set is 5, 5, 5, 5.
Step 2: Calculate the mean (average) of the data set. Since all values are the same, the mean is 5.
Step 3: Subtract the mean from each value in the data set. This gives us: 5-5=0, 5-5=0, 5-5=0, 5-5=0.
Step 4: Square each of the results from Step 3. This gives us: 0^2=0, 0^2=0, 0^2=0, 0^2=0.
Step 5: Calculate the average of these squared differences. The average of 0, 0, 0, 0 is 0.
Step 6: The variance is the result from Step 5, which is 0.

Variance – Variance measures the spread of a set of values; it is calculated as the average of the squared differences from the mean.