# The following is the data of pocket expenditure per week of 50 students in a class. It is known that the median of the distribution is Rs. 120. Find the missing frequencies. - Mathematics and Statistics

Sum

The following is the data of pocket expenditure per week of 50 students in a class. It is known that the median of the distribution is ₹120. Find the missing frequencies.

 Expenditure per week(in ₹) 0 – 50 50 – 100 100 – 150 150 –200 200 –250 No. of students 7 ? 15 ? 3

#### Solution

Let a and b be the missing frequencies of the class 50 – 100 and class 150 – 200 respectively.

We construct the less than cumulative frequency table as given below:

 Expenditure per week (in ₹) No. of students (f) Less than Cumulative frequency(c.f.) 0 – 50 7 7 50 – 100 a 7 + a 100 – 150 15 22 + a ← Q2 150 – 200 b 22 + a + b 200 – 250 3 25 + a + b Total 25 + a + b

Here, N = 25 + a + b
Since, N = 50
∴ 25 + a + b = 50
∴ a + b = 25 ............(i)
Given, Median = Q2 = 120
∴ Q2 lies in the class 100 – 150.
∴ L = 100, h = 50, f = 15, (2"N")/4=(2xx50)/4 = 25,
c.f. = 7 + a

Q2 = "L"+"h"/"f"((2"N")/4-"c.f.")

∴ 120 = 100+(50)/(15)[25-(7+"a")]

∴ 120 – 100 = 10/3(25-7-"a")

∴  20 = 10/3(18-"a")
∴ 60/10 = 18 − a
∴ 6 = 18 – a
∴ a = 18 − 6 = 12
Substituting the value of a in equation (i), we get
12 + b = 25
∴ b = 25 − 12 = 13
∴ 12 and 13 are the missing frequencies of the class 50 – 100 and class 150 – 200 respectively.

Concept: Concept of Median
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