If the data set is: 10, 20, 30, 40, 50, what is the variance?

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Question: If the data set is: 10, 20, 30, 40, 50, what is the variance?

Options:

Correct Answer: 250

Solution:

Mean = 30; Variance = [(10-30)² + (20-30)² + (30-30)² + (40-30)² + (50-30)²] / 5 = 200.

If the data set is: 10, 20, 30, 40, 50, what is the variance?

If the data set is: 10, 20, 30, 40, 50, what is the variance?

Step 1: Find the mean (average) of the data set. Add all the numbers together: 10 + 20 + 30 + 40 + 50 = 150. Then divide by the number of values (5): 150 / 5 = 30.
Step 2: Subtract the mean from each number in the data set and square the result: (10-30)², (20-30)², (30-30)², (40-30)², (50-30)².
Step 3: Calculate each squared difference: (10-30)² = 400, (20-30)² = 100, (30-30)² = 0, (40-30)² = 100, (50-30)² = 400.
Step 4: Add all the squared differences together: 400 + 100 + 0 + 100 + 400 = 1000.
Step 5: Divide the total by the number of values (5) to find the variance: 1000 / 5 = 200.

Mean – The average of a data set, calculated by summing all values and dividing by the number of values.
Variance – A measure of how much the values in a data set differ from the mean, calculated as the average of the squared differences from the mean.
Population vs Sample Variance – Understanding the difference between calculating variance for an entire population versus a sample, which affects the denominator used in the variance formula.