# In the frequency distribution of families given below, the number of families corresponding to expenditure group 2000 - 4000 is missing from the table. However value of 25th percentile is 2880. Find - Mathematics and Statistics

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In the frequency distribution of families given below, the number of families corresponding to expenditure group 2000 - 4000 is missing from the table. However value of 25th percentile is 2880. Find the missing frequency.

 Weekly Expenditure (₹1000) 0 – 2 2 – 4 4 – 6 6 – 8 8 – 10 No. of families 14 ? 39 7 15

#### Solution

Let x be the missing frequency of expenditure group 2000 – 4000.
We construct the less than cumulative frequency table as given below:

 Weekly Expenditure No. of families (f) Less than cumulative frequency (c.f.) 0 – 2000 14 14 2000 – 4000 x 14 + x ← P25 4000 – 6000 39 53 + x 6000 – 8000 7 60 + x 8000 – 10000 15 75 + x Total 75 + x

Here, N = 75 + x
Given, P25 = 2880
∴ P25 lies in the class 2000 – 4000.
∴ L = 2000, h = 2000, f = x, c.f. = 14

∴ P25 = "L"+"h"/"f"((25"N")/100-"c.f.")

∴ 2880 = 2000+2000/"x"((75+"x")/4-14)

∴ 2880 – 2000 =2000/"x"((75+"x"-56)/4)

∴ 880x = 500(x + 19)
∴ 880x = 500x + 9500
∴ 880x – 500x = 9500
∴ 380x = 9500

∴ x = 9500/380 = 25
∴ 25 is the missing frequency of the expenditure group 2000 – 4000.

Concept: Relations Among Quartiles, Deciles and Percentiles
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Chapter 1: Partition Values - Miscellaneous Exercise 1 [Page 21]

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 1 Partition Values
Miscellaneous Exercise 1 | Q 4 | Page 21
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