employee weekly salary anja $245 raz $300 natalie $325 mic $465 paul $100 what is the variance for the data…

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 14,006 17,507.5

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 14,006 17,507.5

Answer

Explanation:

Step1: Calculate the mean

$x_1 = 245$, $x_2=300$, $x_3 = 325$, $x_4=465$, $x_5 = 100$ $n = 5$ $\bar{x}=\frac{245 + 300+325+465+100}{5}=\frac{1435}{5}=287$

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

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

Answer:

17507.5