Find the median income of the following frequency distribution:Weekly Income(Rs.)0 –10001000 –20002000 –30003000 –40004000 –50005000 –6000Frequency 250 190 100 40 15 5
Question
Find the median income of the following frequency distribution:Weekly Income(Rs.)0 –10001000 –20002000 –30003000 –40004000 –50005000 –6000Frequency 250 190 100 40 15 5
Solution
To find the median income, we first need to find the cumulative frequency. The cumulative frequency is the running total of the frequencies.
Here's the cumulative frequency distribution:
| Weekly Income(Rs.) | Frequency | Cumulative Frequency |
|---|---|---|
| 0 –1000 | 250 | 250 |
| 1000 –2000 | 190 | 440 |
| 2000 –3000 | 100 | 540 |
| 3000 –4000 | 40 | 580 |
| 4000 –5000 | 15 | 595 |
| 5000 –6000 | 5 | 600 |
The total frequency (N) is 600. The median is the ((N+1)/2)th value, which is the 300.5th value.
The cumulative frequency just greater than (N+1)/2 = 300.5 is 440. So, the median class is 1000 – 2000.
Now, we can use the formula for median of grouped data:
Median = L + [(N/2 - CF) / F] * C
where: L = Lower boundary of the median group = 1000 N = Total number of data = 600 CF = Cumulative frequency of the group before the median group = 250 F = Frequency of the median group = 190 C = Width of the median group = 1000
Substituting these values in:
Median = 1000 + [(600/2 - 250) / 190] * 1000 Median = 1000 + [50 / 190] * 1000 Median = 1000 + 263.16 Median = 1263.16
So, the median income is Rs. 1263.16.
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