Question

Gabriella asked 5 of her hundreds of coworkers how much storage space they were currently using on their computer. Here are their responses (in gigabytes): 4, 8, 8, 9, 11 The mean of these amounts is overline x=8 gigabytes. What is the standard deviation?

Answer 1

To find the standard deviation, subtract the mean from each amount, square the result, add up the squared results, divide by the total number of amounts, and take the square root of the variance.

Step-by-step explanation:

To find the standard deviation of the storage space, we need to calculate the variance first. The variance is the average of the squared differences between each amount and the mean. So, we subtract the mean from each amount, square the result, and divide by the total number of amounts. Then, we take the square root of the variance to get the standard deviation. Here are the steps:

1. Subtract the mean (8) from each amount: -4, 0, 0, 1, 3
2. Square each result: 16, 0, 0, 1, 9
3. Add up the squared results: 16 + 0 + 0 + 1 + 9 = 26
4. Divide by the total number of amounts (5): 26 / 5 = 5.2
5. Take the square root of the variance: sqrt(5.2) ≈ 2.28

Therefore, the standard deviation of the storage space is approximately 2.28 gigabytes.