Question

five friends want to compare the number of minutes it takes each of minutes it takes each of them to complete the same puzzle. the data results, in minutes, are shown. 8,5,11,10,6. what is the stanadard deviation of the data set? round to the nearest hundreth.

Answer 1

Therefore, the standard deviation of the data set is approximately 2.28 (rounded to the nearest hundredth).

Explanation:

To find the standard deviation of the data set, we will follow these steps:

1. Calculate the mean:

- Add up all the numbers in the data set: 8 + 5 + 11 + 10 + 6 = 40

- Divide the sum by the total number of values: 40 / 5 = 8

2. Calculate the difference from the mean for each data point:

- For each data point, subtract the mean from the data point:

8 - 8 = 0

5 - 8 = -3

11 - 8 = 3

10 - 8 = 2

6 - 8 = -2

3. Square each difference:

- Square each difference calculated in the previous step:

0^2 = 0

(-3)^2 = 9

3^2 = 9

2^2 = 4

(-2)^2 = 4

4. Calculate the mean of the squared differences:

- Add up all the squared differences: 0 + 9 + 9 + 4 + 4 = 26

- Divide the sum by the total number of values: 26 / 5 = 5.2

5. Calculate the square root of the mean of squared differences:

- Take the square root of the result from step 4: √5.2 ≈ 2.28