The scores of a test are: 20, 30, 40, 50. What is the standard deviation? (2020)

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Question: The scores of a test are: 20, 30, 40, 50. What is the standard deviation? (2020)

Options:

Correct Answer: 15

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 = 125. SD = √125 = 11.18 (approx 10).

The scores of a test are: 20, 30, 40, 50. What is the standard deviation? (2020)

The scores of a test are: 20, 30, 40, 50. What is the standard deviation? (2020)

Step 1: Add all the test scores together: 20 + 30 + 40 + 50.
Step 2: Divide the total from Step 1 by the number of scores (4) to find the mean: (20 + 30 + 40 + 50) / 4.
Step 3: Subtract the mean from each score to find the difference: 20 - mean, 30 - mean, 40 - mean, 50 - mean.
Step 4: Square each of the differences you found in Step 3.
Step 5: Add all the squared differences together.
Step 6: Divide the total from Step 5 by the number of scores (4) to find the variance.
Step 7: Take the square root of the variance from Step 6 to find the standard deviation.

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.
Standard Deviation – The square root of the variance, representing the average distance of each data point from the mean.