INTRODUCTION & FINDING MEDIAN OF AN UNGROUPED DATA
MEDIAN – The value of the middle most observation obtained after arranging the data in an ascending order, is called median of the data.
Median Of An Ungrouped Data –
Arrange the given data in ascending order.
Let, the total number of observations be ‘n’. Then,
n + 1
Median = (--------)th observation, when ‘n’ is odd.
2
1 n n
Median = [----- {(-----)th observation + (------ + 1)th observation}],
2 2 2
when ‘n’ is even.
Example.1) The runs scored by 11 members of a cricket team are –
32, 58, 17, 37, 34, 33, 12, 0, 47, 20, 40
Find the median score
Ans.) Arranging the given numbers in an ascending order, we get –
0, 12, 17, 20, 32, 33, 34, 37, 40, 47, 58.
Here, n = 11, which is odd.
n + 1
Median Score = (-------)th observation
2
11 + 1
= (--------)th Observation
2
12
= (-------)th Obervation
2
= 6th observation = 33
Hence, the median score is 33. (Ans.)
Example.2) The heights of the 10 students (in Kg) are –
40, 47, 54, 31, 43, 38, 51, 53, 36, 34
Find the median weight.
Ans.) Arranging the given weights in an ascending orders, we get –
31, 34, 36, 38, 40, 43, 47, 51, 53, 54.
Here n = 10, which is even,
1 n n
Median = ------ X {(-----)th observation + (----- + 1)th observation}
2 2 2
1 10 10
= ----- X {(------)th observation + (------ + 1)th observation}
2 2 2
1
= ------- (5th observation + 6th observation)
2
1 83
= ----------- (40 + 43) = ------- = 41.5 Kg
2 2
Hence, the median weight is 41.5 Kg (Ans.)
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