The scores of a test are: 20, 30, 40, 50. Calculate the variance. (2020)

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Question: The scores of a test are: 20, 30, 40, 50. Calculate the variance. (2020)

Options:

Correct Answer: 200

Exam Year: 2020

Solution:

Mean = (20 + 30 + 40 + 50) / 4 = 35. Variance = [(20-35)² + (30-35)² + (40-35)² + (50-35)²] / 4 = 250.

The scores of a test are: 20, 30, 40, 50. Calculate the variance. (2020)

The scores of a test are: 20, 30, 40, 50. Calculate the variance. (2020)

Step 1: Add all the test scores together: 20 + 30 + 40 + 50.
Step 2: Calculate the total: 20 + 30 + 40 + 50 = 140.
Step 3: Count how many scores there are: There are 4 scores.
Step 4: Calculate the mean (average) by dividing the total by the number of scores: 140 / 4 = 35.
Step 5: Subtract the mean from each score to find the difference: (20 - 35), (30 - 35), (40 - 35), (50 - 35).
Step 6: Calculate the differences: -15, -5, 5, 15.
Step 7: Square each difference: (-15)² = 225, (-5)² = 25, (5)² = 25, (15)² = 225.
Step 8: Add the squared differences together: 225 + 25 + 25 + 225 = 500.
Step 9: Divide the total of the squared differences by the number of scores to find the variance: 500 / 4 = 125.

Mean – The average of a set of numbers, calculated by summing the values and dividing by the count.
Variance – A measure of how much the values in a set differ from the mean, calculated as the average of the squared differences from the mean.
Squared Differences – The result of subtracting the mean from each value, then squaring the result to eliminate negative values.