Question

The test scores for a math class are shown below.

81, 85, 82, 93, 85, 84, 95, 87, 88, 91
What is the standard deviation of the data set? Round your answer to the nearest tenth.

Answer 1

To find the standard deviation of a data set, we first need to calculate the mean (average) of the data set.

Mean (average) = (81 + 85 + 82 + 93 + 85 + 84 + 95 + 87 + 88 + 91) / 10
Mean = 881 / 10
Mean = 88.1

Next, we calculate the variance by finding the squared differences between each data point and the mean, then averaging these squared differences.

Variance = [(81 - 88.1)^2 + (85 - 88.1)^2 + (82 - 88.1)^2 + (93 - 88.1)^2 + (85 - 88.1)^2 + (84 - 88.1)^2 + (95 - 88.1)^2 + (87 - 88.1)^2 + (88 - 88.1)^2 + (91 - 88.1)^2] / 10
Variance = (49.21 + 9.61 + 38.44 + 26.01 + 9.61 + 21.16 + 47.61 + 1.21 + 0.01 + 7.21) / 10
Variance = 200.08 / 10
Variance = 20.008

Finally, we find the standard deviation by taking the square root of the variance.

Standard deviation = √20.008
Standard deviation ≈ 4.5

Therefore, the standard deviation of the data set is approximately 4.5.