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

Answer:

$\bar X= \frac{1930055}{110}=17545.95$

Step-by-step 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:

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

Where $n = \sum_{i=1}^n f_i = 110$

So then if we replace into the formula we got:

$\bar X= \frac{1930055}{110}=17545.95$