A data set has values: 10, 12, 14, 16. What is the variance? (2021)

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Question: A data set has values: 10, 12, 14, 16. What is the variance? (2021)

Options:

Correct Answer: 4

Exam Year: 2021

Solution:

Mean = (10 + 12 + 14 + 16) / 4 = 13. Variance = [(10-13)² + (12-13)² + (14-13)² + (16-13)²] / 4 = 2.5.

A data set has values: 10, 12, 14, 16. What is the variance? (2021)

A data set has values: 10, 12, 14, 16. What is the variance? (2021)

Step 1: Add all the values together: 10 + 12 + 14 + 16.
Step 2: Calculate the total: 10 + 12 + 14 + 16 = 52.
Step 3: Count how many values there are: There are 4 values.
Step 4: Calculate the mean (average) by dividing the total by the number of values: 52 / 4 = 13.
Step 5: Subtract the mean from each value to find the difference: (10 - 13), (12 - 13), (14 - 13), (16 - 13).
Step 6: Calculate the differences: -3, -1, 1, 3.
Step 7: Square each difference: (-3)² = 9, (-1)² = 1, (1)² = 1, (3)² = 9.
Step 8: Add the squared differences together: 9 + 1 + 1 + 9 = 20.
Step 9: Divide the total of squared differences by the number of values to find the variance: 20 / 4 = 5.

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