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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 - 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
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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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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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