For the data set: 5, 7, 8, 9, 10, what is the standard deviation?

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Question: For the data set: 5, 7, 8, 9, 10, what is the standard deviation?

Options:

Correct Answer: 2

Solution:

Mean = 7.5; Variance = [(5-7.5)^2 + (7-7.5)^2 + (8-7.5)^2 + (9-7.5)^2 + (10-7.5)^2] / 5 = 2; Standard Deviation = sqrt(2) = 1.41

For the data set: 5, 7, 8, 9, 10, what is the standard deviation?

For the data set: 5, 7, 8, 9, 10, what is the standard deviation?

Step 1: Find the mean (average) of the data set. Add all the numbers together: 5 + 7 + 8 + 9 + 10 = 39. Then divide by the number of values (5): 39 / 5 = 7.5.
Step 2: Calculate the variance. For each number, subtract the mean (7.5) and square the result: (5 - 7.5)^2, (7 - 7.5)^2, (8 - 7.5)^2, (9 - 7.5)^2, (10 - 7.5)^2.
Step 3: Perform the calculations: (5 - 7.5)^2 = 6.25, (7 - 7.5)^2 = 0.25, (8 - 7.5)^2 = 0.25, (9 - 7.5)^2 = 2.25, (10 - 7.5)^2 = 6.25.
Step 4: Add these squared results together: 6.25 + 0.25 + 0.25 + 2.25 + 6.25 = 15.
Step 5: Divide the total (15) by the number of values (5) to find the variance: 15 / 5 = 3.
Step 6: Find the standard deviation by taking the square root of the variance: sqrt(3) ≈ 1.73.

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