find the standard deviation of the data set below. if necessary, round tot he nearest hundredth. 79, 82, 88, 88, 92, 92, 95, 96, 98 question 19 2 pts find the standard deviation of the data set below. if necessary, round tot he nearest hundredth. 26, 33, 43, 25, 35, 46, 37, 31, 28, 37 question 20 2 pts find the standard deviation of the data set below. if necessary, round tot he nearest hundredth. 9, 9, 11, 12, 15, 17, 17, 20, 20, 21, 22

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Accepted Answer

# Explanation:
## Step1: Calculate the mean
For the first data set $79,82,88,88,92,92,95,96,98$:
The mean $\bar{x}=\frac{79 + 82+88+88+92+92+95+96+98}{9}=\frac{810}{9} = 90$
For the second data set $26,33,43,25,35,46,37,31,28,37$:
The mean $\bar{x}=\frac{26+33 + 43+25+35+46+37+31+28+37}{10}=\frac{341}{10}=34.1$
For the third data set $9,9,11,12,15,17,17,20,20,21,22$:
The mean $\bar{x}=\frac{9+9+11+12+15+17+17+20+20+21+22}{11}=\frac{173}{11}\approx15.73$

## Step2: Calculate the variance
For the first data set:
$$
\begin{align*}
s^{2}&=\frac{(79 - 90)^{2}+(82-90)^{2}+(88 - 90)^{2}+(88 - 90)^{2}+(92-90)^{2}+(92 - 90)^{2}+(95-90)^{2}+(96-90)^{2}+(98-90)^{2}}{9-1}\
&=\frac{(-11)^{2}+(-8)^{2}+(-2)^{2}+(-2)^{2}+2^{2}+2^{2}+5^{2}+6^{2}+8^{2}}{8}\
&=\frac{121 + 64+4+4+4+4+25+36+64}{8}\
&=\frac{326}{8}=40.75
\end{align*}
$$
The standard deviation $s=\sqrt{40.75}\approx6.38$

For the second data set:
$$
\begin{align*}
s^{2}&=\frac{(26-34.1)^{2}+(33 - 34.1)^{2}+(43-34.1)^{2}+(25-34.1)^{2}+(35-34.1)^{2}+(46-34.1)^{2}+(37-34.1)^{2}+(31-34.1)^{2}+(28-34.1)^{2}+(37-34.1)^{2}}{10 - 1}\
&=\frac{(-8.1)^{2}+(-1.1)^{2}+8.9^{2}+(-9.1)^{2}+0.9^{2}+11.9^{2}+2.9^{2}+(-3.1)^{2}+(-6.1)^{2}+2.9^{2}}{9}\
&=\frac{65.61+1.21 + 79.21+82.81+0.81+141.61+8.41+9.61+37.21+8.41}{9}\
&=\frac{434.9}{9}\approx48.32
\end{align*}
$$
The standard deviation $s=\sqrt{48.32}\approx6.95$

For the third data set:
$$
\begin{align*}
s^{2}&=\frac{(9-15.73)^{2}+(9 - 15.73)^{2}+(11-15.73)^{2}+(12-15.73)^{2}+(15-15.73)^{2}+(17-15.73)^{2}+(17-15.73)^{2}+(20-15.73)^{2}+(20-15.73)^{2}+(21-15.73)^{2}+(22-15.73)^{2}}{11-1}\
&=\frac{(-6.73)^{2}+(-6.73)^{2}+(-4.73)^{2}+(-3.73)^{2}+(-0.73)^{2}+1.27^{2}+1.27^{2}+4.27^{2}+4.27^{2}+5.27^{2}+6.27^{2}}{10}\
&=\frac{45.2929+45.2929+22.3729+13.9129+0.5329+1.6129+1.6129+18.2329+18.2329+27.7729+39.3129}{10}\
&=\frac{234.19}{10}=23.419
\end{align*}
$$
The standard deviation $s=\sqrt{23.419}\approx4.84$

# Answer:
First data set: $6.38$
Second data set: $6.95$
Third data set: $4.84$

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Question

Explanation:

Step1: Calculate the mean

Step2: Calculate the variance

Answer: