The median of the following data is 16 Find the missing frequencies a and b if the total of - Maths -

Question

The median of the following data is 16 Find the missing frequencies
a and b if the total of frequencies is 70

Class
0−5
5 −10
10 −15
15−20
20 −25
25−30
30 −35
35−40

Frequency
12
a
12
15
b
6
6
4

Global Expert · Accepted Answer

We prepare the cumulative frequency table, as shown below:

Class

Frequency (fi)

Cumulative frequency (cf)

0−5
12
12

5−10
a
12 + a

10−15
12
24 + a

15−20
15
39 + a

20−25
b
39 + a +
b

25−30
6
45 + a + b

30−35
6
51 + a + b

35−40
4
55 + a + b

Total
N =
∑fi = 70

Let a and b be the missing frequencies of class intervals
5−10 and
20−25 respectively
Then,

55 + a + b = 70
⇒ a + b = 15
(1)

Median is 16, which lies in 15−20 So, the median class is
15−20

∴ l = 15, h = 5, N = 70,
f = 15 and cf = 24 + a

Now,

Median=l+N2-cff×h⇒16=15+702-24+a15×5⇒16=15+35-24-a3⇒16=15+11-a3⇒16-15=11-a3⇒1×3=11-a⇒a=11-3⇒a=8

∴ b = 15 −
a [From (1)]
⇒ b = 15 − 8
⇒ b = 7

Hence, a = 8 and b = 7

Class	0−5	5 −10	10 −15	15−20	20 −25	25−30	30 −35	35−40
Frequency	12	a	12	15	b	6	6	4

The median of the following data is 16. Find the missing frequencies a and b if the total of frequencies is 70. Class 0−5 5 −10 10 −15 15−20 20 −25 25−30 30 −35 35−40 Frequency 12 a 12 15 b 6 6 4