Question

Find the standard deviation for the following test scores: 22, 99, 102, 33, 57, 75, 100, 81, 62, 29. Which score contributes most to the deviation from the mean?

A) 33
B) 102
C) 22
D) 75

Answer 1

To find the standard deviation of the test scores, you calculate the mean, find deviations, square them, average them, and take the square root of the average.

Step-by-step explanation:

The standard deviation for the given test scores (22, 99, 102, 33, 57, 75, 100, 81, 62, 29) can be found by following these steps:

1. Calculate the mean (average) of the test scores.
2. Subtract the mean from each test score to find the deviation for each score.
3. Square each deviation to get the squared deviations.
4. Calculate the mean of the squared deviations.
5. Take the square root of the mean of the squared deviations to get the standard deviation.

Let's do the calculations:

1. The mean is (22 + 99 + 102 + 33 + 57 + 75 + 100 + 81 + 62 + 29) / 10 = 66.0.
2. Deviations: (22-66.0), (99-66.0), (102-66.0), etc.
3. Squared deviations: (-44)^2, (33)^2, (36)^2, etc.
4. The mean of the squared deviations: (1944 + 1089 + 1296 + ... + 1369) / 10.
5. The square root of the mean of the squared deviations gives us the standard deviation.

To determine which score contributes most to the deviation from the mean, we calculate the absolute value of each deviation (since squaring eliminated negative signs) and compare them. We are seeking the largest of these absolute values.

The exact number has been left out because it's expected that computations would be carried out by a graphing calculator or computer software. However, it is clear that test score B) 102, being the farthest from the mean, contributes most to the standard deviation.