Question

7. In 1980 a college paid its 52 instructors a mean salary of $13, 200, its 96 assistant professors a
mean salary of Rs.55, 800, its 67 associate professors a mean salary of Rs.88, 900, and its 35
full professors a mean salary of Rs.123,500. What was the mean salary paid to all the teaching
staff of this college?​

Answer 1

Given :- In 1980 a college paid its 52 instructors a mean salary of Rs.13, 200, its 96 assistant professors a mean salary of Rs.55, 800, its 67 associate professors a mean salary of Rs.88, 900, and its 35 full professors a mean salary of Rs.123,500. What was the mean salary paid to all the teaching staff of this college ?

Solution :-

→ Mean salary of 52 instructors = Rs.13, 200

so,

→ Total salary of 52 instructors = 52 * 13200 = Rs. 686,400

and,

→ Mean salary of 96 assistant professors = Rs.55800

so,

→ Total salary of 96 assistant professors = 96 * 55800 = Rs.5,356,800

and,

→ Mean salary of 67 associate professors = Rs.88900

so,

→ Total salary of 67 associate professors = 67 * 88900 = Rs.5956300

and,

→ Mean salary of 35 full professors = Rs. 123,500

so,

→ Total salary of 35 full professors = 35 * 123500 = Rs.4322500 .

then ,

→ Mean salary paid to all the teaching staff of this college = Total salary of all teachers / Total number of teachers = (686400 + 5356800 + 5956300 + 4322500) / (52 + 96 + 67 + 35) = 16322000 / 250 = Rs.65288 (Ans.)

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Answer 2

Given : In 1980 a college paid its 52 instructors a mean salary of Rs.13, 200, its 96 assistant professors a mean salary of Rs.55, 800,

its 67 associate professors a mean salary of Rs.88, 900, and

its 35 full professors a mean salary of Rs.123, 500.

To Find : What was the mean salary paid to all the teaching staff of this college?

​

Solution:

Mean  = ∑fx/∑f

∑fx  = 52 * 13200 + 96 * 55800 + 67 * 88900 + 35 * 123500

=>  ∑fx  = 1,63,22,000

∑f  = 52 + 96 + 67 + 35   = 250

Mean Salary =  1,63,22,000 / 250

= 65,288

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