# The median of the following incomplete table is 92. Find the missing frequencies: C.I. 30 – 50 50 – 70 70 – 90 90 – 110 110 – 130 130 –150 Total f 6 ? 18 20 ? 10 80 - Mathematics and Statistics

Sum

The median of the following incomplete table is 92. Find the missing frequencies:

 C.I. 30 – 50 50 – 70 70 – 90 90 – 110 110 – 130 130 – 150 Total f 6 ? 18 20 ? 10 80

#### Solution

Let a and b be the missing frequencies of the class 50 – 70 and class 110 – 130 respectively.
We construct the less than cumulative frequency table as given below:

 C.I. f Less than cumulative frequency (c.f.) 30 – 50 6 6 50 – 70 a 6 + a 70 – 90 18 24 + a 90 – 110 20 44 + a ← Q2 110 – 130 B 44 + a + b 130 – 150 10 54 + a + b Total N = 80

Here, N = 54 + a + b
Since, N = 80
∴ 54 + a + b = 80
∴ a + b = 26  .........(i)
Given, Median = Q2 = 92
∴ Q2 lies in the class 90 – 110.

∴ L = 90, h = 20, f = 20, (2"N")/4=(2xx80)/4 = 40, c.f. = 24 + a

∴ Q2 = "L"+"h"/"f"((2"N")/4-"c.f.")

∴ 92 = 90 + 20/20[40 - (24 + "a")]

∴ 92 – 90 = 40 – 24 – a
∴ 2 = 16 – a
∴ a = 14
Substituting the value of a in equation (i), we get
14 + b = 26
∴ b = 26 – 14 = 12
∴ 14 and 12 are the missing frequencies of the class 50 – 70 and class 110 – 130 respectively.

Concept: Concept of Median
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 1 Partition Values
Miscellaneous Exercise 1 | Q 13 | Page 22