Question

question 4 of 10
for the data set 6, 5, 10, 11, 13, the mean, \\(\bar{x}\\), is 9. what is the standard deviation?

the formula for the sample standard deviation is
\\(s = \sqrt{\frac{1}{n - 1}\sigma (x - \bar{x})^2}\\).

use the table to help you.

\\(x\\)	\\(x - \bar{x}\\)	\\((x - \bar{x})^2\\)
5	-4	16
10	1	1
11	2	4
13	4	16
		sum = 46

round your answer to the nearest tenth.

\\(\bigcirc\\) a. 3.4
\\(\bigcirc\\) b. 3
\\(\bigcirc\\) c. 11.25
\\(\bigcirc\\) d. 9.2

Explanation:

Step1: Identify n, sum of (x - x̄)²

n (number of data points) is 5. Sum of \((x - \bar{x})^2\) is 46 (from table).

Step2: Apply sample std dev formula

Sample standard deviation formula: \( s = \sqrt{\frac{1}{n - 1}\sum (x - \bar{x})^2} \). Substitute n = 5, sum = 46: \( s = \sqrt{\frac{46}{5 - 1}} = \sqrt{\frac{46}{4}} \).

Step3: Calculate and round

\(\frac{46}{4} = 11.5\), so \( s = \sqrt{11.5} \approx 3.4 \) (rounded to nearest tenth).

Answer:

A. 3.4