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Question
If the arithmetic mean of the data given below is 28, find the median of the series:
|
Profit per retail shop (in Rs) |
0 - 10 |
10 - 20 |
20 - 30 |
30 - 40 |
40 - 50 |
50 - 60 |
|
Number of retail shops |
12 |
18 |
27 |
- |
17 |
6 |
Solution
|
Class Interval |
Frequency (f) |
Cumulative Frequency (CF) |
|
0 - 10 |
12 |
12 |
|
10 - 20 |
18 |
30 |
|
20 - 30 |
27 |
57 |
|
30 - 40 |
20 |
77 |
|
40 - 50 |
17 |
94 |
|
50 - 60 |
6 |
100 |
|
Total |
`sumf=100` |
`sumf="N"=100`
So, the Median class = Size of `("N"/2)^"th"` item
= 50th item
50th item lies in the 57th cumulative frequency and the corresponding class interval is 20 - 30.
Median `=L+(N/2-CF)/fxxi`
`=20+(100/2-30)/27xx10`
`=20+(50-30)/27xx10`
`=20+20/27xx10`
= 27.40
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