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 14,006 17,507.5

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:

$17,507.5$