4 The city of Pottsville has 8 police officers on the payrol

4. The city of Pottsville has 8 police officers on the payroll. The annual salaries for these police officers are listed below $22,000 $38,000 $40,000 $28,000 $32,000 $45,000 $38,000 Compute the mean, median and mode salary for these police officers. $40,000

Solution

1. mean of the data = (sum of all the observations) / number of observations

=> ($22,000 + $38,000 + $40,000 + $28,000 + $32,000 + $45,000 + $38,000 + $40,000) / 8

=>$283,000 / 8

=>$35,375.

2. median of the data

first let us arrange the data in ascending order,

$22,000 . $28,000 , $32,000 , $38,000, $38,000 , $40,000 , $40,000 , $45,000.

median of the data is the middle most value of the data set.

here,

since the data set is even number, i.e 8 observations,

the median will be the average of the two middle most numbers,

two middle most numbers = $38,000 and $38,000.

median = ($38,000 + $38,000) / 2

=>$38,000.

3.mode of the data,

mode of the data is that item which repeats frequently than any other item in the observation,

It is possible to have no mode, it none of the item repeats greater than any other item.

It is also possible to have more than one mode, if more than one item repeat for same number of times.

In the given set of observations,

$38,000 and $40,000 repeat two times each.

Therfore it can be said that the given set of data is a bimodal data, with ($38,000 and $40,000) being the modes.

in the given set of data $38,000