# CLASS-10FINDING MEDIAN OF AN UNGROUPED DATA

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.)