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Calculation of Median – Discrete series
Q. 7. From the following data, find the value
of median:
| x |
8 |
5 |
6 |
10 |
9 |
4 |
7 |
| f |
6 |
4 |
5 |
8 |
9 |
6 |
4 |
Solution. To locate the middle items, we first
compute the cumulative frequencies after arranging
the values of x in ascending order.
| x |
f |
Cumulative frequency
(cf) |
| 4
|
6 |
6 |
| 5
|
4 |
10
|
| 6
|
5 |
15
|
| 7
|
4 |
19
|
| 8
|
6 |
25
|
| 9
|
9 |
34
|
| 10
|
8 |
42
|
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Total
|
42
|
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Number of observations is 42 (even).
There are two middle items, (42/2 )th and [(42/2)
+ 1 ]th, i.e., 21st and 22nd
items. The value of each of them is 8, since the value
of each item 20th to 25th is
8.
Therefore, median = mean of 21st and 22nd
items.
(8 + 8)/2 = 8.
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