for the data set 6, 5, 10, 11, 13, the mean, $\bar{x}$, is 9. what is the standard deviation?\nthe formula…

for the data set 6, 5, 10, 11, 13, the mean, $\bar{x}$, is 9. what is the standard deviation?\nthe formula for the sample standard deviation is $s = sqrt{\frac{1}{n - 1}sum(x - \bar{x})^2}$.\nuse the table to help you.\n|$x$|$x-\bar{x}$|$(x - \bar{x})^2$|\n|----|----|----|\n|6|-3|9|\n|5|-4|16|\n|10|1|1|\n|11|2|4|\n|13|4|16|\n|sum = | |46|\nround your answer to the nearest tenth.\na. 9.2\nb. 11.25\nc. 3.4\nd. 3

for the data set 6, 5, 10, 11, 13, the mean, $\bar{x}$, is 9. what is the standard deviation?\nthe formula for the sample standard deviation is $s = sqrt{\frac{1}{n - 1}sum(x - \bar{x})^2}$.\nuse the table to help you.\n|$x$|$x-\bar{x}$|$(x - \bar{x})^2$|\n|----|----|----|\n|6|-3|9|\n|5|-4|16|\n|10|1|1|\n|11|2|4|\n|13|4|16|\n|sum = | |46|\nround your answer to the nearest tenth.\na. 9.2\nb. 11.25\nc. 3.4\nd. 3

Answer

Explanation:

Step1: Identify values

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

Step2: Apply standard - deviation formula

The formula for the sample standard deviation is $s=\sqrt{\frac{1}{n - 1}\sum(x-\bar{x})^2}$. Substitute $n = 5$ and $\sum(x-\bar{x})^2 = 46$ into the formula: [ \begin{align*} s&=\sqrt{\frac{46}{5 - 1}}\ &=\sqrt{\frac{46}{4}}\ &=\sqrt{11.5}\ &\approx3.4 \end{align*} ]

Answer:

C. 3.4