Question

question 2 of 10
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 = sqrt(1/(n - 1)sum(x - x)^2).
use the table to help you.
round your answer to the nearest tenth.
a. 3
b. 3.4
c. 9.2
d. 11.25

Explanation:

Step1: Identify the values from the formula

We have \(n = 5\) (the number of data points), and \(\sum(x-\bar{x})^2=46\) from the table.

Step2: Substitute into the formula

Substitute \(n = 5\) and \(\sum(x-\bar{x})^2 = 46\) into \(s=\sqrt{\frac{1}{n - 1}\sum(x-\bar{x})^2}\). First, calculate \(n-1=5 - 1=4\). Then \(\frac{1}{n - 1}\sum(x-\bar{x})^2=\frac{46}{4}=11.5\).

Step3: Calculate the square - root

\(s=\sqrt{11.5}\approx3.4\) (rounded to the nearest tenth).

Answer:

B. 3.4