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Question
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.
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