MEDIAN OF UNGROUPED DATA –
MEDIAN -
After arranging the given data in an ascending and descending order of magnitude, the value of the middle most observation is called the median of the data.
Method for finding the Median of an Ungrouped Data –
First of all, we have to arrange the given data in an increasing or decreasing order of magnitude. Let the total number of observations be ‘n’.
n + 1
i) If, n is odd, then median would be = value of (-------)th observation.
2
ii) If, n is even, then median =
1 n n
----- {(------)th observation + (------ + 1)th observation}
2 2 2
There are some examples are given below for your better understanding -
Example.1) The marks of 15 students (out of 50) in an examinations are –
26, 32, 39, 23, 21, 17, 33, 41, 18, 25, 30, 24, 27, 9, 36. Find the median marks.
Ans.) Arranging the marks in an ascending order, we have –
9, 17, 18, 21, 23, 24, 25, 26, 27, 30, 32, 33, 36, 39, 41.
Here, n = 15, which is odd
1
So, here median marks = value of ------- (15 + 1)th term
2
= value of 8th term = 26 (Ans.)
Example.2) The weight (in kg) of 12 children are –
52, 46, 42, 38, 49, 55, 53, 41, 47, 43, 45, 48. Find the median weight
And.) Arranging the weights is ascending order, we have –
38, 41, 42, 43, 45, 46, 47, 48, 49, 52, 53, 55.
Here, n = 12, which is even
1 12 12
So, median weight = ------ {(-------)th term + (------- + 1)th term}
2 2 2
1
= ------- (6th term + 7th term)
2
1 93
= ------- (46 + 47) = ------- = 46.5 kg
2 2
Hence median weight = 46.5 kg (Ans.)