For the data set 6, 5, 10, 11, 13, the mean, x, is 9. What is the standard deviation?The formula for the sample standard deviation is 𝑠=1𝑛−1Σ(𝑥−𝑥ˉ)2s= n−11​ Σ(x− xˉ ) 2 ​ .Use the table to help you.Round your answer to the nearest tenth.

To calculate the standard deviation, we first need to find the differences between each data point and the mean, square these differences, sum them up, divide by the number of data points minus 1, and finally take the square root.

Here are the steps:

1. Calculate the differences between each data point and the mean: 6 - 9 = -3 5 - 9 = -4 10 - 9 = 1 11 - 9 = 2 13 - 9 = 4

2. Square these differences: (-3)^2 = 9 (-4)^2 = 16 1^2 = 1 2^2 = 4 4^2 = 16

3. Sum up these squared differences: 9 + 16 + 1 + 4 + 16 = 46

4. Divide by the number of data points minus 1: 46 / (5 - 1) = 46 / 4 = 11.5

5. Take the square root of this result: sqrt(11.5) = 3.4 (rounded to the nearest tenth)

So, the standard deviation of the data set is approximately 3.4.