Median and mode

1. Median & Mode
By
Dr. Abhishek Srivastava

2. Median is a centrally located value of a series such that half of
the values (or items) of the series are above it and the other half
below it.
• मेडियन एक श्रृंखला का केंद्र रूप से डथित मूल्य है जैसे डक श्रृंखला के
मान (या आइटम) का आधा डहथसा इसके ऊपर और दूसरा आधा इसके
नीचे है।
Formula:-
• M=Size of (N+1/2)th item
Calculate Median From Following
• 2,3,4,6,7,8,9,
MEDIAN

3. • 2,3,4,6,7,8,9,
• Size =7
• Median = Size of (N+1/2)th item
• = 4th item
• =6

4. Calculate Median From Following
2,3,4,5, 6,7,8,9,
Solution
Median = N/2 And N/2+1 th Term
Median= 4th & 5th term
Median= 5,6
Median= 5.5

5. Formula:- M=l1 +( N / 2-c.f.)/f x i

6. e) INCULDING SERIES AND THE MEDIAN
ILLUSTRATION.
Calculate median of the following data:
Solution:- This is an inclusive series given in the descending order. It shouldbe
converted into an exclusive series and place in the ascending order, as in the
following tables:
Marks 46-50 41-45 36-40 31-35 26-30 21-25 16-20 11-15
No. of
students
5 11 22 35 26 13 10 7
Conversion into Exclusive
Series
10.5 – 15.5
15.5 – 20.5
20.5 – 25.5
25.5 – 30.5
(l1) 30.5 – 35.5
35.5 – 40.5
40.5 – 45.5
45.5 – 50.5
Frequency Cumulative frequency
(f)
7 7
10 17
13 30
26 56 (c.f.)
35 (f) 91
22 113
11 124
5 129
N = 129

7. • Median, M = Size of (N/2)th item; N=∑𝑓 =129
• = Size of (129/2)th item = Size of 64.5th item
• Using the formula,
• M = l1 + (N/2 - c.f.)/f x i
• =30.5+(129/2-56)/35 x 5
• =30.5+(64.5-56/35) x 5
• =30.5+8.5/35 x 5
• =30.5+1.2
• =31.7
• Median = 31.7 marks.

8. 6. MEDIAN OF THE SERIES WITH UNEQUAL CLASSINTERVALS
ILLUSTRATION:- Calculating median of the following distribution of data:
Solution :
Estimation of Median
CLASS INTERVAL 0-5 5-10 10-20 20-30 30-50 50-70 70-100
NUMBER OF
STUDENTS
12 15 25 40 42 14 8
Class Interval Frequency (f) Cumulative
Frequency
12 12
15 27
25 52 (c.f.)
40 (f) 92
42 134
14 148
0 – 5
5 – 10
10 – 20
(l1) 20 – 30
30 – 50
50 – 70
70 - 100 8 156
N = 156

9. M = Size of (N/2)th item; N = 156
= Size of (156/2)th item = Size of 78th item
this lies in 92th cumulative frequency and the corresponding median class is
20-30.
:- l1 = 20, c.f. = 52 , f = 40 and i = 10
substituting the values in the formula, we have
M = l1 + (N/2-c.f./f) x i
= 20 + (156/2-52/40) x 10
= 20 +( 78-52/40) x 10
= 20 +(26/40) x 10
= 20 +6.5
= 26.5
Median =26.5

10. • The number which appears most often in a set of
numbers.
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 (it
occurs most often).
MODE
.

11. Calculate Mode From Following
2,3,9,4,6,7,9,8,9,8,6, 9
Mode =9

12. Thanks