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Question
The following table gives the monthly consumption of electricity of 100 families:
| Monthly Consumption (in units) |
130 – 140 | 140 – 150 | 150 – 160 | 160 – 170 | 170 – 180 | 180 – 190 | 190 – 200 |
| Number of families |
5 | 9 | 17 | 28 | 24 | 10 | 7 |
Find the median of the above data.
Solution
From the given table,
| Monthly Consumption |
Number of Families (f) |
Cumulative frequency (C.f.) |
| 130 – 140 | 5 | 5 |
| 140 – 150 | 9 | 14 |
| 150 – 160 | 17 | 31 |
| 160 – 170 | 28 | 59 |
| 170 – 180 | 24 | 83 |
| 180 – 190 | 10 | 93 |
| 190 – 200 | 7 | 100 |
We have, N = 100
`N/2` = 50
Median class = 160 – 170
`\implies` l = 160, f = 28, Cf = 31, h = 10
Median = `l + [((N/2 - Cf))/f] xx h`
= `160 + [((50 - 31))/28] xx 10`
= `160 + [19/28] xx 10`
= 160 + 6.78
= 166.78
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