Median example (Grouped data):
Let’s consider the following frequency distribution that shows the exam scored receive by 40 students in a certain class:
|
Exam Score (xi) |
(fi) |
CF |
|
51-60 |
9 |
9 |
|
61-70 |
7 |
16 |
|
71-80 |
15 |
31 |
|
81-90 |
6 |
37 |
|
90-100 |
3 |
40 |
Here, n= 40.
Therefore, n/2 = 40/2
= 20
Thus, the
observations lie between the class interval 61-70, which is called the median
class.
Therefore,
Lower class limit = 61
Class size, h = 10
Frequency of the
median class, f = 7
Cumulative frequency
of the class preceding the median class, CF = 16.
Now, substituting the values in the median formula
given above, we get
Median= 61 + (20-16)/7 *10 = 66.71
Therefore, the median marks for the given data are 66.71.
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