Question

Compute the variance and standard deviation of the sample data shown below. 7 2 8 4 6 2 13.

Answer 1

The variance of the sample data is 15, and the standard deviation is approximately 3.9. The value one standard deviation below the mean is 2.1.

Step-by-step explanation:

To compute the variance and standard deviation of the sample data (7, 2, 8, 4, 6, 2, 13), first calculate the sample mean.

1. Add all the numbers: 7 + 2 + 8 + 4 + 6 + 2 + 13 = 42.
2. Divide the sum by the number of data points: 42 / 7 = 6. This is the sample mean.
3. Find the deviations from the mean for each data point and square these deviations.
4. Add up all the squared deviations: (1+16+4+4+0+16+49) = 90.
5. To calculate the sample variance, divide this sum by the number of data points minus one. So, 90 / (7 - 1) = 90 / 6 = 15.
6. Finally, calculate the sample standard deviation by taking the square root of the variance: √15 ≈ 3.9 (rounded to the nearest tenth).

Now, to find the value that is one standard deviation below the mean, subtract the standard deviation from the mean: 6 - 3.9 = 2.1.