Question

The standard deviation for the sample scores 63, 74, 82, 75, 93, 86, and 80 is approximately ______, indicating the degree of variability or dispersion in the data.

1) 7.89
2) 6.75
3) 9.12
4) 5.43

Answer 1

The standard deviation for the sample scores 63, 74, 82, 75, 93, 86, and 80 is approximately 8.24.

Step-by-step explanation:

The standard deviation for the sample scores 63, 74, 82, 75, 93, 86, and 80 can be calculated using the following steps:

1. Find the mean (average) of the sample scores: (63 + 74 + 82 + 75 + 93 + 86 + 80) / 7 = 80.286.
2. Subtract the mean from each score and square the result: (63 - 80.286)^2, (74 - 80.286)^2, (82 - 80.286)^2, (75 - 80.286)^2, (93 - 80.286)^2, (86 - 80.286)^2, (80 - 80.286)^2.
3. Find the mean of the squared differences: (63 - 80.286)^2 + (74 - 80.286)^2 + (82 - 80.286)^2 + (75 - 80.286)^2 + (93 - 80.286)^2 + (86 - 80.286)^2 + (80 - 80.286)^2 / 7 = 67.857.
4. Take the square root of the mean squared differences to find the standard deviation: √67.857 ≈ 8.240.

Therefore, the standard deviation for the sample scores is approximately 8.24, indicating the degree of variability or dispersion in the data.