Question

employee weekly salary anja $245 raz $300 natalie $325 mic $465 paul $100 what is the variance for the data? variance $s^{2}=\frac{(x_{1}-overline{x})^{2}+(x_{2}-overline{x})^{2}+cdots+(x_{n}-overline{x})^{2}}{n - 1}$ 118.35 132.32 14006 17507.5

Explanation:

Step1: Calculate the mean

The data set is \(245,300,325,465,100\). The mean \(\bar{x}=\frac{245 + 300+325+465+100}{5}=\frac{1435}{5}=287\).

Step2: Calculate the squared - differences

\((245 - 287)^2=( - 42)^2 = 1764\), \((300 - 287)^2=13^2 = 169\), \((325 - 287)^2 = 38^2=1444\), \((465 - 287)^2=178^2 = 31684\), \((100 - 287)^2=( - 187)^2=34969\).

Step3: Calculate the sum of squared - differences

\(1764+169+1444+31684+34969 = 70030\).

Step4: Calculate the variance

Using the formula \(s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}\), with \(n = 5\), we have \(s^{2}=\frac{70030}{4}=17507.5\).

Answer:

17507.5