Question

A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the
mean salary.
Salary ($) Employees
5,001-10,000 16
10,001-15,000 14
15,001-20,000 15
20,001-25,000 17
25,001-30,000 18

Answer 1

Answer:

$\bar X = \frac{1435040}{80}=17938$

Step-by-step explanation:

Since we have a groued data for this case we can construct the following table to find the expected value.

 Interval               Frequency(fi)      Midpoint(xi)           xi*fi

5001-10000              16                       7500.5            120008

10001-15000             14                      12500.5           175007

15001-20000            15                      17500.5           262507.5

20001-25000           17                      22500.5          382508.5

25001-30000           18                      27500.5          495009

Total                          80                                              1435040

And we can calculate the mean with the following formula:

$\bar X = \frac{\sum_{i=1}^n f_i x_i}{n}$

Where $n=\sum_{i=1}^n f_i = 80$

And if we replace we got:

$\bar X = \frac{1435040}{80}=17938$