8. The following series relates to the daily income of working employed in a firm. Compute
(1) highest income of lowest 50% workers (ii) minimum income earned by the top 25% of the
workers, and (iv) maximum income earned by lowest 25% workers:
Daily Income (Rs.):
10-14
15-19
20-24
25-29
30-34
35-39
No. of Workers:
5
10
15
20
10
5
[Hint: Compute Median, Upper Quartile and Lower Quartile]
[Ans. (i) Rs. 25.11 (ii) Rs. 29.19 (iii) Rs. 19.92]
Answers
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Answer:
Interval No. of Workers
(f
i
) Class Mark (x
i
) Deviation
d
i
=
h
x
i
−A
f
i
d
i
20−24 2 22 −2 −4
25−29 10 27 −1 −10
$30 - 34$$ 15 32→A 0 0
35−39 20 37 1 20
40−49 28 42 2 56
45−49 25 47 3 75
Total
∑f
i
=100
∑f
i
d
i
=137
Assumed Mean (A)=32 and h=5
∴ Mean(
x
)=A+
∑f
i
h∑f
i
d
i
x
=32+
100
5×137
=32+6.85
=38.85
Explanation:
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