Includes solved numerical problems on Median, in three series individual, discrete and continuous. Moreover, it consists some unsolved problems for practice after learning.

1. MEDIAN
Median is the value which divides the series into two equal parts. Thus in the case
of median, the number of terms less than the median value and the number of terms
more than the median value, are equal.
Median is a positional measure. The position which is exactly in the centre, equal
number of terms lie on either side of it, when terms are arranged in ascending or
descending order.
Median is a statistical measure that determines the middle value of a dataset listed
in ascending order (i.e., from smallest to largest value). The measure divides the
lower half from the higher half of the dataset. Along with mean and mode, median
is a measure of central tendency.
According to Prof. L.R. Conner, “The median is that value of the variable which
divides the group into two equal parts, one part comprising all values greater and
the other all values less than median.”
Calculation of Median
I. Individual series
When number of terms is odd (1,3,7,5,9)
1. 5,7,9,12,10,8,7,15,21.
Arrange in ascending or descending order;
5,7,7,8,9,10,12,15,21.
N= 9
Now, M= N+1th term
2
= 9+1 th term
2
= 10/2
= 5th
term
M= 9

2. When number of terms is even (2,4,6,8,10)
2. 13,17,29,18,24,21,31,27,34,25.
Arrange in ascending or descending order;
13,17,18,21,24,25,27,29,31,34.
N= 10
Now, M= N+1th term
2
= 10+1 th term
2
= 11/2 = 5.5th
term
= 5th
term+ 6th
term
2
= 24+25
2
M = 24.5
Or
5.5th
term
5th
term +.5 (6th
term-5th
term)
24 +.5 (25-24) = 24.5
Do it yourself:
Calculate median from the following figures:
1. 28,47,30,37,54,58,61,64,31,34,52,55,62. (Ans. 52)
2. 10,18,9,17,15,24,30,11. (Ans. 16)
3. 60,35,48,52,26,27,47,50. (Ans. 47.5)
4. 17,32,35,32,15,21,42,11,10,18. (Ans. 19.5)
II. Discrete series
1. Calculate the value of median:
X 10 20 30 40 50 60 70
f 4 7 21 34 25 12 3

3. x f cf terms
10 4 4 1-4
20 7 4+7=11 5-11
30 21 11+21=32 12-32
40 34 32+34=66 33-66 53.5
50 25 66+25=91 67-91
60 12 91+12=103 92-103
70 3 103+3=106 104-106
N=106
M= size of {N+1}th term
2
= {106+1}th term
2
=107/2 th term
=53.5th
term (53.5 lies between 33-66)
Thus, M= 40.
Do it yourself
Calculate median:
1.
X 10 20 30 40 50 60 70
f 2 3 5 10 5 3 2
(Ans. 40)
2.
Size 105 110 115 120 125 130 135
f 2 3 4 6 10 5 2
(Ans. 125)
III. Continuous series
C.I. f cf terms
1-3 6 6 1-6
3-5 53 6+53=59 7-59
5-7 85 59+85=144 60-144
7-9 56 144+56=200 145-200
9-11 21 200+21=221 201-221

4. 11-13 16 221+16=237 222-237
13-15 4 237+4=241 238-241
15-17 4 241+4=245 242-245
M= L+ N1-cf X i
F
N= 245
N1 = N/2
245/2= 122.5
Cf= 59
F=85
i= 2
l= 5
M= 5 + 122.5-59 X 2
85
M= 5+ 63.5 X 2
85
M= 5 + 1.5
M= 6.5 Ans.
Do it yourself:
1.
C.I. 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50
f 22 45 67 73 85 190 64 55
(Ans. 35.22)
2.
X 10-25 25-40 40-55 55-70 70-85 85-100
f 6 50 44 26 3 1
(Ans. 43.07)
E-notes by:
Asst. Prof. Harpreet Kaur