For the question below, use the following set of scores: 82, 60, 78, 81, 65, 72, 72, 78. What is the standard deviation? Round to the nearest hundredth.

To find the standard deviation of a set of scores, we need to follow these steps:

Step 1: Find the mean of the set of scores.
Step 2: Calculate the deviation of each score from the mean.
Step 3: Square each deviation.
Step 4: Find the mean of the squared deviations.
Step 5: Take the square root of the mean of the squared deviations.

Let's calculate the standard deviation using these steps:

Step 1: Find the mean of the set of scores.
mean = (82 + 60 + 78 + 81 + 65 + 72 + 72 + 78) / 8
mean = 68.75

Step 2: Calculate the deviation of each score from the mean.
deviation of each score = score - mean

For our set of scores, the deviations are:
(82 - 68.75), (60 - 68.75), (78 - 68.75), (81 - 68.75), (65 - 68.75), (72 - 68.75), (72 - 68.75), (78 - 68.75)
13.25, -8.75, 9.25, 12.25, -3.75, 3.25, 3.25, 9.25

Step 3: Square each deviation.
squared deviations = (13.25)^2, (-8.75)^2, (9.25)^2, (12.25)^2, (-3.75)^2, (3.25)^2, (3.25)^2, (9.25)^2
175.56, 76.56, 85.56, 150.06, 14.06, 10.56, 10.56, 85.56

Step 4: Find the mean of the squared deviations.
mean of squared deviations = (175.56 + 76.56 + 85.56 + 150.06 + 14.06 + 10.56 + 10.56 + 85.56) / 8
mean of squared deviations = 60.9961

Step 5: Take the square root of the mean of the squared deviations.
Standard deviation = \sqrt{60.9961}
Standard deviation ≈ 7.81

Answer: The standard deviation of the given set of scores, rounded to the nearest hundredth, is 7.81.