For the data set: 5, 7, 9, 11, 13, what is the variance?

For the data set: 5, 7, 9, 11, 13, what is the variance?

Step 1: Find the mean (average) of the data set. Add all the numbers together: 5 + 7 + 9 + 11 + 13 = 45. Then divide by the number of values (5): 45 / 5 = 9.
Step 2: Subtract the mean from each number in the data set and square the result: (5-9)² = 16, (7-9)² = 4, (9-9)² = 0, (11-9)² = 4, (13-9)² = 16.
Step 3: Add all the squared results together: 16 + 4 + 0 + 4 + 16 = 40.
Step 4: Divide the total from Step 3 by the number of values (5) to find the variance: 40 / 5 = 8.

Mean Calculation – The mean is the average of the data set, calculated by summing all values and dividing by the number of values.
Variance Calculation – Variance measures the spread of the data points around the mean, calculated as the average of the squared differences from the mean.