use the display of data items to find the standard deviation. the standard deviation is (do not round until the final answer. then round to two decimal places as needed)

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Accepted Answer

# Explanation:
## Step1: List out the data
From the histogram, the data set is $6,6,9,9,9,9,9,9,12$.
## Step2: Calculate the mean $\bar{x}$
The mean $\bar{x}=\frac{6 + 6+9+9+9+9+9+9+12}{9}=\frac{75}{9}=\frac{25}{3}\approx8.33$
## Step3: Calculate the variance $s^{2}$
$$
\begin{align*}
s^{2}&=\frac{(6-\frac{25}{3})^{2}+(6 - \frac{25}{3})^{2}+6\times(9-\frac{25}{3})^{2}+(12-\frac{25}{3})^{2}}{9-1}\
&=\frac{(-\frac{7}{3})^{2}+(-\frac{7}{3})^{2}+6\times(\frac{2}{3})^{2}+(\frac{11}{3})^{2}}{8}\
&=\frac{\frac{49}{9}+\frac{49}{9}+6\times\frac{4}{9}+\frac{121}{9}}{8}\
&=\frac{\frac{49 + 49+24 + 121}{9}}{8}\
&=\frac{\frac{243}{9}}{8}\
&=\frac{27}{8}=3.375
\end{align*}
$$
## Step4: Calculate the standard deviation $s$
The standard deviation $s=\sqrt{s^{2}}=\sqrt{3.375}\approx1.84$

# Answer:
$1.84$

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Question

Explanation:

Step1: List out the data

Step2: Calculate the mean \(\bar{x}\)

Step3: Calculate the variance \(s^{2}\)

Step4: Calculate the standard deviation \(s\)

Answer: