The following data shows the wages of 44 workers in a factory. If the
median wage of a worker is Rs. 470. Find x and y in the following.
36.
No. of Workers
Wages (in Rs.)
3
X
200-300
300-400
400-500
nxa ao
500-600
6
600-700
Answers
Answer :-
Wages(in Rs.) --------No. of workers(f) -------- CF
200-300 -------------------- 3 ----------------------- 3
300-400 ------------------- x -------------------- (3 + x)
400-500 ------------------- 20 ------------------(23 + x)
500-600 -------------------- y------------------ (23 + x + y)
600-700 -------------------- 6 ----------------- (29 + x + y)
⅀ fi = 44
so,
→ (29 + x + y) = 44
→ x + y = 44 - 29
→ x + y = 15 ---------------- Eqn.(1)
now,
→ N/2 = 44/2 = 22 .
so,
→ CF just greater than N/2 = (23 + x) .
then, Median class is 400 - 500 .
we have, now,
- L = Lower limit of median class = 400 .
- N/2 = 22 .
- CF = preceding median class = (3 + x)
- F = frequency of median class = 20 .
- h = class size = 100 .
putting all values we get,
→ L + [ {(N/2) - CF}/F ] * h = Median
→ 400 + [{22 - (3 + x)}/20] * 100 = 470
→ {(19 - x)/20} * 100 = 470 - 400
→ 5(19 - x) = 70
→ 19 - x = 14
→ x = 19 - 14
→ x = 5 (Ans.)
putting value of x in Eqn.(1), we get,
→ 5 + y = 15
→ y = 15 - 5
→ y = 10 (Ans.)
Learn more :-
calculate the median and mode from the following income between (rs)100-200 100-300 100-400 100-500 100-600 no of person...
https://brainly.in/question/23585381
Some students of class X donated for the welfare of old age persons. The contributions are shown in the following distri...
https://brainly.in/question/17314012