Question

Find the mean of the data summarized in the given frequency distribution. A company had 110 employees whose salaries are summarized in the frequency distribution below. Find the mean salary. Round to the nearest hundredth. Salery ($) Employees 5,001-10,000 27 10,001-15,000 23 15,001-20,000 12 20,001-25,000 18 25,001-30,000 30

Answer 1

`\bar X= (1930055)/(110)=17545.95`

Explanation:

For this case we can construct the following table in order to find the mean for the grouped data:

Interval Frequency (fi) Midpoint (Xi) Xi *fi

5001-10000 27 7500.5 202513.5

10001-15000 23 12500.5 287511.5

15001-20000 12 17500.5 210006

20001-25000 18 22500.5 405009

25001-30000 30 27500.5 825015

Total 110 1930055

And the mean is calculated with the following formula:

`\bar X= (\sum_(i=1)^n x_i f_i)/(n)`

Where
`n = \sum_(i=1)^n f_i = 110`

So then if we replace into the formula we got:

`\bar X= (1930055)/(110)=17545.95`