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Question 3.20: Teacher Strikes The number of public school teacher strikes ......

Teacher Strikes

The number of public school teacher strikes in Pennsylvania for a random sample of school years is shown. Find the sample variance and the sample standard deviation.

9     10     14     7     8     3

Source: Pennsylvania School Board Association.

Step-by-Step
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Step 1 Find the mean of the data values.

\bar{X}=\frac{\Sigma X}{n}=\frac{9+10+14+7+8+3}{6}=\frac{51}{6}=8.5

Step 2 Find the deviation for each data value (X-\bar{X}).

\begin{aligned}& 9-8.5=0.5 \quad 10-8.5=1.5 \quad 14-8.5=5.5 \\& 7-8.5=-1.5 \quad 8-8.5=-0.5 \quad 3-8.5=-5.5 \end{aligned}

Step 3 Square each of the deviations (X-\bar{X})^2.

\begin{aligned}(0.5)^2 & =0.25 & (1.5)^2 & =2.25 & (5.5)^2 & =30.25 \\(-1.5)^2 & =2.25 & (-0.5)^2 & =0.25 & (-5.5)^2 & =30.25\end{aligned}

Step 4 Find the sum of the squares.

\Sigma(X-\bar{X})^2=0.25+2.25+30.25+2.25+0.25+30.25=65.5

Step 5 Divide by n-1 to get the variance.

s^2=\frac{\Sigma(X-\bar{X})^2}{n-1}=\frac{65.5}{6-1}=\frac{65.5}{5}=13.1

Step 6 Take the square root of the variance to get the standard deviation.

s=\sqrt{\frac{\Sigma(X-\bar{X})^2}{n-1}}=\sqrt{13.1} \approx 3.6 \text { (rounded) }

Here the sample variance is 13.1, and the sample standard deviation is 3.6.

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