Question

1. 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. (round final answer to the nearest tenths.) 8, 10, 14, 8, 2, 5. sample variance: 22.6 sample standard deviation: 4.8 none of the above sample variance: 18.8 sample standard deviation: 8.17 sample variance: 4.8 sample standard deviation: 22.6

Explanation:

Step1: Calculate the mean

The data set is \(8, 10, 14, 8, 2, 5\). The mean \(\bar{x}=\frac{8 + 10+14+8+2+5}{6}=\frac{47}{6}\approx7.83\).

Step2: Calculate the squared - differences

\((8 - 7.83)^2=(0.17)^2 = 0.0289\), \((10 - 7.83)^2=(2.17)^2=4.7089\), \((14 - 7.83)^2=(6.17)^2 = 38.0689\), \((8 - 7.83)^2=(0.17)^2 = 0.0289\), \((2 - 7.83)^2=(- 5.83)^2=34.0889\), \((5 - 7.83)^2=(-2.83)^2 = 8.0089\).

Step3: Calculate the sum of squared - differences

\(S=\sum_{i = 1}^{n}(x_i-\bar{x})^2=0.0289+4.7089+38.0689+0.0289+34.0889+8.0089 = 84.9334\).

Step4: Calculate the sample variance

The sample variance \(s^2=\frac{S}{n - 1}=\frac{84.9334}{6 - 1}=\frac{84.9334}{5}=16.98668\approx17.0\).

Step5: Calculate the sample standard deviation

The sample standard deviation \(s=\sqrt{s^2}=\sqrt{16.98668}\approx4.1\).

Since none of the given options match the calculated values:

Answer:

None of the above