The following frequency distribution is classified according to the number of mangoes in different branches. Calculate the median of the mangoes in each branch
Number of Mangoes $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$
Branch $5$ $4$ $6$ $2$ $4$ $3$ $1$

37.68

37.68

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36.87

36.87

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38.76

38.76

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25.83

37.86

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Solution

The correct option is D $25.83$
37.86

Number of mangoes

Branch (f)

cf

0-10

5

5

10-20

4

9

20-30

6

15

30-40

2

17

40-50

4

21

50-60

3

22

60-70

1

25

So $n = 25$
So, $\frac{n}{2} = \frac{25}{2} = 12.5$
$12.5$ is nearest to $15 (c u m u l a t i v e f r e q u e n c y)$
Observation lies in the class $20 - 30$
$l = 20, c f = 9, f = 6, h = 5$
$M e d i a n == l + ⎛ ⎜ ⎜ ⎝ \frac{\frac{n}{2} - c f}{f} ⎞ ⎟ ⎟ ⎠ \times h = 20 + (\frac{12.5 - 9}{6}) \times 10 = 20 + \frac{3.5}{6} \times 10 = 20 + \frac{35}{6} = 20 + 5.83 = 25.83 A n s$

Suggest Corrections

Variable	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	Total
Frequency	$12$	$30$	$f_{1}$	$65$	$f_{2}$	$25$	$18$	$229$

Number of Mangoes	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Branch	$5$	$4$	$6$	$2$	$4$	$3$	$1$

X (Rs. in 000)	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Y (Frequency)	$2$	$3$	$6$	$5$	$2$	$2$

Marks	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$3$	$7$	$10$	$6$	$8$	$2$	$4$

Class	$0 - 10$	$10 - 20$	$20 - 30$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$5$	$4$	$3$	$2$	$2$	$1$	$1$

$C I$	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
$f$	$12$	$18$	$6$	$10$	$8$	$25$	$22$	$4$