A data set has values: 2, 4, 4, 4, 5, 5, 7, 9. What is the variance? (2021)

A data set has values: 2, 4, 4, 4, 5, 5, 7, 9. What is the variance? (2021)

Step 1: List the values in the data set: 2, 4, 4, 4, 5, 5, 7, 9.
Step 2: Calculate the mean (average) of the data set. Add all the values together: 2 + 4 + 4 + 4 + 5 + 5 + 7 + 9 = 40. Then divide by the number of values (8): 40 / 8 = 5.
Step 3: Subtract the mean from each value to find the difference: (2-5), (4-5), (4-5), (4-5), (5-5), (5-5), (7-5), (9-5). This gives: -3, -1, -1, -1, 0, 0, 2, 4.
Step 4: Square each of the differences: (-3)² = 9, (-1)² = 1, (-1)² = 1, (-1)² = 1, (0)² = 0, (0)² = 0, (2)² = 4, (4)² = 16. This gives: 9, 1, 1, 1, 0, 0, 4, 16.
Step 5: Add all the squared differences together: 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32.
Step 6: Divide the total by the number of values (8) to find the variance: 32 / 8 = 4.

Variance Calculation – Understanding how to compute variance from a data set, including finding the mean and applying the formula for variance.
Mean Calculation – Calculating the mean of a data set as a prerequisite for finding variance.