Calculate the variance of the data set {2, 4, 4, 4, 5, 5, 7, 9}.

Calculate the variance of the data set {2, 4, 4, 4, 5, 5, 7, 9}.

Step 1: Write down the data set: {2, 4, 4, 4, 5, 5, 7, 9}.
Step 2: Calculate the mean (average) of the data set. Add all the numbers together: 2 + 4 + 4 + 4 + 5 + 5 + 7 + 9 = 40.
Step 3: Divide the total by the number of values in the data set. There are 8 numbers, so: 40 / 8 = 5. The mean is 5.
Step 4: Subtract the mean from each number in the data set and square the result:
- (2 - 5)² = (-3)² = 9
- (4 - 5)² = (-1)² = 1
- (4 - 5)² = (-1)² = 1
- (4 - 5)² = (-1)² = 1
- (5 - 5)² = (0)² = 0
- (5 - 5)² = (0)² = 0
- (7 - 5)² = (2)² = 4
- (9 - 5)² = (4)² = 16.
Step 5: Add all the squared results together: 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32.
Step 6: Divide the total squared result by the number of values in the data set (8): 32 / 8 = 4.
Step 7: The variance of the data set is 4.

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.
Population vs Sample Variance – Understanding whether to use population variance (dividing by N) or sample variance (dividing by N-1) is crucial.