## Chapter 3

## Q. 3.21

**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 sample standard deviation.

9, 10, 14, 7, 8, 3

## Step-by-Step

## Verified Solution

**Step 1** Find the sum of the values:

ΣX = 9 + 10 + 14 + 7 + 8 + 3 = 51

**Step 2** Square each value and find the sum:

ΣX² = 9² + 10² + 14² + 7² + 8² + 3² = 499

**Step 3** Substitute in the formula and solve:

\begin{aligned}s^2 & =\frac{n\left(\Sigma X^2\right)-(\Sigma X)^2}{n(n-1)} \\& =\frac{6(499)-51^2}{6(6-1)}\end{aligned}

\begin{aligned}& =\frac{2994-2601}{6(5)} \\& =\frac{393}{30} \\& =13.1\end{aligned}

The variance is 13.1.

s=\sqrt{13.1} \approx 3.6 \text { (rounded) }

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

Notice that these are the same results as the results in Example 3–20.