Question

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

Answer 1

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.