the weekly salaries of a sample of employees at the local bank are given in the table below.\n| employee |…

the weekly salaries of a sample of employees at the local bank are given in the table below.\n| employee | weekly salary |\n| anja | $245 |\n| raz | $300 |\n| natalie | $325 |\n| mic | $465 |\n| paul | $100 |\nwhat is the variance for the data?\nvariance: $s^{2}=\frac{(x_{1}-overline{x})^{2}+(x_{2}-overline{x})^{2}+cdots+(x_{n}-overline{x})^{2}}{n - 1}$

the weekly salaries of a sample of employees at the local bank are given in the table below.\n| employee | weekly salary |\n| anja | $245 |\n| raz | $300 |\n| natalie | $325 |\n| mic | $465 |\n| paul | $100 |\nwhat is the variance for the data?\nvariance: $s^{2}=\frac{(x_{1}-overline{x})^{2}+(x_{2}-overline{x})^{2}+cdots+(x_{n}-overline{x})^{2}}{n - 1}$

Answer

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).

It seems there is an error in the provided options as the correct variance value calculated above is (17507.5). If we assume this is a sample variance calculation and there was a mis - typing in the problem setup or options, and we recalculate with the correct understanding of the formula application for the given data.

Let's re - check the formula application.

The mean (\bar{x}=\frac{245+300 + 325+465+100}{5}=287)

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

Sum of squared differences (S=\sum_{i = 1}^{5}(x_i-\bar{x})^2=1764 + 169+1444+31684+34969=70030)

Variance (s^2=\frac{S}{n - 1}=\frac{70030}{4}=17507.5)

If we assume this is a population variance (though the problem seems to imply a sample with the (n-1) in the formula), the formula would be (\sigma^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n})

(\sigma^{2}=\frac{70030}{5}=14006)

Since the problem uses the (n - 1) formula, we stick with the sample variance calculation and the value (17507.5)

If we assume there is a calculation error in our steps and re - calculate:

Mean (\bar{x}=\frac{245 + 300+325+465+100}{5}=287)

((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)

Sum (=1764+169+1444+31684+34969 = 70030)

Sample variance (s^2=\frac{70030}{4}=17507.5)

If we made a wrong assumption and it's a population variance (\sigma^{2}=\frac{70030}{5}=14006)

Since the problem has the (n - 1) formula in the variance formula box, we consider it a sample variance problem and the answer is (17507.5)

Answer:

There is an error in the provided options as the correct variance value is (17507.5) (assuming sample variance calculation as per the given formula (s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}))