Question

employee weekly salary anja $245 raz $300 natalie $325 mic $465 paul $100 what is the variance for the data? variance: $s^{2}=\frac{(x_{1}-overline{x})^{2}+(x_{2}-overline{x})^{2}+cdots+(x_{n}-overline{x})^{2}}{n - 1}$ 110.35 132.32 14,006 17,507.5

Explanation:

Step1: Calculate the mean

Let \(x_1 = 245\), \(x_2=300\), \(x_3 = 325\), \(x_4=465\), \(x_5 = 100\). The number of data - points \(n = 5\). The mean \(\bar{x}=\frac{245 + 300+325+465+100}{5}=\frac{1435}{5}=287\).

Step2: Calculate the squared differences

\((x_1-\bar{x})^2=(245 - 287)^2=(-42)^2 = 1764\)
\((x_2-\bar{x})^2=(300 - 287)^2=(13)^2 = 169\)
\((x_3-\bar{x})^2=(325 - 287)^2=(38)^2 = 1444\)
\((x_4-\bar{x})^2=(465 - 287)^2=(178)^2 = 31684\)
\((x_5-\bar{x})^2=(100 - 287)^2=(-187)^2 = 34969\)

Step3: Calculate the sum of squared differences

\(\sum_{i = 1}^{n}(x_i-\bar{x})^2=1764+169+1444+31684+34969=70030\)

Step4: Calculate the variance

The variance \(s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}=\frac{70030}{4}=17507.5\)

Answer:

17,507.5