Question

In: Statistics and Probability

A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the...

A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the mean salary.

SALARY FREQUENCY
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
Group of answer choices

17,500

17,937.50

19,731.25

16,143.75

Solutions

Expert Solution

We have to mean salary for the given data -

Formula for mean -


Obervation table -

Here, we will require midpoint of classes to find mean. For finding midpoint, we have to first convert classes into exclusive type.

To convert classes into exclusive type, we add & subtract to upper & lower limits of classes by difference of upper limit of class & lower limit of next class divided by 2. i.e. (Lower limit of next class - Upper limit of first class)/2

So, (10001 - 10000)/2 = 1/2 = 0.5

Hence, we have to substract 0.5 from lower limit & add 0.5 to upper limit.

Formula for midpoint -

Observation table -

Class Exclusive Class Midpoint(x) frequency (f) xf
5001-10000 5000.5-10000.5 7500.5 16 120000
10001-15000 10000.5-15000.5 12500.5 14 175000
15001-20000 15000.5-20000.5 17500.5 15 262500.5
20001-25000 20000.5-25000.5 22500.5 17 382500.5
25001-30000 25000.5-30000.5 27500.5 18 495000
Total - - 80 1435000

Calculations -

Where,

,

So,

Mean salary is 17937.5.

Option B is correct.


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