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Question
Find the mean, median and mode of the following data:
| Classes: | 0-20 | 20-40 | 40-60 | 40-60 | 80-100 | 100-120 | 120-140 |
| Frequency: | 6 | 8 | 10 | 12 | 6 | 5 | 3 |
Solution
Consider the following data.
| Class | Frequency (fi) | xi | fi xi | C.f. |
| 0−20 | 6 | 10 | 60 | 6 |
| 20−40 | 8 | 30 | 240 | 14 |
| 40−60 | 10 | 50 | 500 | 24 |
| 60−80 | 12 | 70 | 840 | 36 |
| 80−100 | 6 | 90 | 540 | 42 |
| 100−120 | 5 | 110 | 550 | 47 |
| 120−140 | 3 | 130 | 390 | 50 |
| `N=sumf=50` | `sumf_1x_1=3120` |
Here, the maximum frequency is 12 so the modal class is 60−80.
Therefore,
l = 60
h = 20
f = 12
f1 = 10
f2 = 6
F = 24
Median `=l+(N/2-F)/fxxh`
`=60+(25-24)/12xx20`
`=60+1/12xx20`
`=60+20/12`
= 60 + 1.67
= 61.67
Thus, the median of the data is 61.66.
Mean `=(sumf_1x_1)/sumf`
`=3120/50=32.4`
Thus, the mean of the data is 62.4.
Mode `=l+(f-f1)/(2f-f1-f2)xxh`
`=60+(12-10)/(24-10-6)xx20`
`=60+2/8xx20`
`=60+40/8`
= 60 + 5
= 65
Thus, the mode of the data is 65.
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