## Q. 3.20

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.

## Verified Solution

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.