The scores of five students are: 20, 22, 24, 26, 28. Calculate the variance. (20

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Question: The scores of five students are: 20, 22, 24, 26, 28. Calculate the variance. (2020)

Options:

Correct Answer: 8

Exam Year: 2020

Solution:

Mean = (20 + 22 + 24 + 26 + 28) / 5 = 24. Variance = [(20-24)² + (22-24)² + (24-24)² + (26-24)² + (28-24)²] / 5 = 8.

The scores of five students are: 20, 22, 24, 26, 28. Calculate the variance. (2020)

The scores of five students are: 20, 22, 24, 26, 28. Calculate the variance. (2020)

Step 1: Add all the scores together: 20 + 22 + 24 + 26 + 28.
Step 2: Calculate the total: 20 + 22 = 42, 42 + 24 = 66, 66 + 26 = 92, 92 + 28 = 120.
Step 3: Divide the total by the number of students (5) to find the mean: 120 / 5 = 24.
Step 4: Subtract the mean from each score to find the difference: (20 - 24), (22 - 24), (24 - 24), (26 - 24), (28 - 24).
Step 5: Calculate the differences: -4, -2, 0, 2, 4.
Step 6: Square each difference: (-4)² = 16, (-2)² = 4, 0² = 0, 2² = 4, 4² = 16.
Step 7: Add the squared differences together: 16 + 4 + 0 + 4 + 16.
Step 8: Calculate the total of the squared differences: 16 + 4 = 20, 20 + 0 = 20, 20 + 4 = 24, 24 + 16 = 40.
Step 9: Divide the total of the squared differences (40) by the number of students (5) to find the variance: 40 / 5 = 8.

Mean Calculation – The mean is calculated by summing all scores and dividing by the number of scores.
Variance Calculation – Variance measures the spread of scores around the mean, calculated as the average of the squared differences from the mean.
Understanding of Squared Differences – It is crucial to correctly compute the squared differences from the mean for each score.