Mean mode median formulas

1. Introduction to Statistics
• Definition of Statistics:-
It is the branch of science which deals with collection, representation,
analyzing and interpretation of data.
•Application and Scope:-
1. Statistics in Business
2. Statistics in Economics and Commerce
3. Statistics in Social Science
4. Statistics in Management Science
• Average:-
Average is a measure of central tendency which can give a
single value from a group of values to represent them in a
systematic way.

2. Mean:-
Mean is the average value of the observation if x1, x2, x3,-----
----xn are the observations then the arithmetic meanx is given by.
Formula: x = x1 + x2+ x3+ ---- xn
n
x = xi
n
Example:- 9, 18, 12, 7, 11, 23, 21 find out mean.
Solution:-
x = 9+18+12+7+11+23+21
7
x = 101
7
x = 14.42
So, Mean is 14.42

3. Median:-
Median is the middle value of the observation which
devides the total observation in 2 parts.
Example 1:-
X = 5, 13, 18, 35, 61
 N = 5
 Median = 18 (Middle Value)
Example 2:-
X = 12, 15, 16, 19, 24, 27
 N = 6
 Median = 16+19
2
= 35
2
= 17.5
Formula No 02 :-
Median = l+ h N
So, Median is
17.5
f 2
C

4. Mode:-
Mode is the value which occurs most frequently (maximum times) in
a set of observation.
Formula 1:- Mode = most repeated item
Example 1:- 11, 15, 22, 12, 11 ,13, 11, 21, 31, 14, 13, 11, 14, 13, 11
 Mode = 11
Formula 2:-
Mode = l+h (f1 – f2)
2f1- f0 – f2
Where, l = lower limit of module class
h = difference between 2 class
f1 = frequency of module class
f2 = frequency of succeeding module class
f0 = frequency of preceding (prior)class
Formula 3:-
Relationship between mean, median and mode.
Mean- Mode = 3 (Mean- Median)

5. 



Class Frequency (F) Class width (X) Xifi C. F
0 -10 4 5 20 4
10 -20 2 15 30 6
20-30 18 25 450 24
30-40 22 35 770 46
40-50 21 45 940 67
50-60 19 55 1045 86
60-70 10 65 650 96
70-80 3 75 225 99
80-90 1 85 85 100
fi (N) =100 xifi = 4220
Example2:- Calculate the mean, median and mode for the following frequency distribution.
(Mean) X = xifi
fi
= 4220
100
= 42.20
So, Mean is 42.20

6. Median = N = 100 = 50
2 2
So, the nearest value to so is 46.i.e. c.f. so,
median class is 30-40.
Median = L+h n
f 2
C
= 30 + 10 (50-24)
22
= 30 + 10  26
22
= 30 + 11.82
= 41.82
Mean - Mode = 3 (Mean - Median)
42.20 - Mode = 3 ( 42.20 – 41.82)
Mode = 42.20 – 1.14
Mode = 41.06

7. Represented by:
Nikhil D. Patel
Pankaj S. Bhadane