For the data set: 10, 12, 14, 16, what is the variance? (2019)

For the data set: 10, 12, 14, 16, what is the variance? (2019)

Step 1: Add all the numbers in the data set: 10 + 12 + 14 + 16.
Step 2: Calculate the total: 10 + 12 + 14 + 16 = 52.
Step 3: Count how many numbers are in the data set: There are 4 numbers.
Step 4: Calculate the mean (average) by dividing the total by the count: 52 / 4 = 13.
Step 5: Subtract the mean from each number in the data set: (10 - 13), (12 - 13), (14 - 13), (16 - 13).
Step 6: Calculate the results of the subtractions: -3, -1, 1, 3.
Step 7: Square each of the results: (-3)² = 9, (-1)² = 1, (1)² = 1, (3)² = 9.
Step 8: Add the squared results together: 9 + 1 + 1 + 9 = 20.
Step 9: Divide the total of the squared results by the count of numbers: 20 / 4 = 5.
Step 10: The variance of the data set is 5.

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