Calculation of Mean, Median, Mode, Variance & Standard Deviation For Grouped Data
Calculation of Mean, Median, Mode, Variance & Standard Deviation For Grouped Data
Calculation of Mean, Median, Mode, Variance & Standard Deviation For Grouped Data
Freque
ncy
10
20
30
20
10
Solution:
For Median:
To find out median we always find median group first.
How to find median group?
To find out median group calculate (f/2) and then find this value in (C.f) column
where it lies that class would be our required median group.
Note: f/2 = 45 lies in 3rd class (those values which lie in between 31 to 60 lies in
3rd class)
Class
18
19
20
21
20
Total
()
Freque
ncy
(f)
10
20
Cumulative
frequency
(C.f)
10
30
30
20
10
60
80
90
Median
group
f = 90
Calculation of Median:
Above frequency distribution is simple frequency distribution where we dont have
class intervals so, to find out median simply picked class value of median group i.e.,
20.
Median = 20
For Mode:
To find out median we always find median group first.
How to find mode group?
To find out mode group find maximum frequency, where it lies that class would be
our required mode group.
Note: if 2 or more classes have a same maximum frequency then there would be 2
or more mode groups which mean 2 or more mode lies in data subsequently.
18
19
Frequen
cy
(f)
10
20
20
21
20
30
20
10
Class
Mode
group
Calculation of Mode:
Above frequency distribution is a simple frequency distribution where we dont have
class intervals so, to find out mode simply picked class value of mode group i.e., 20.
Mode = 20
Mean=
fx
f
variance=
2
fx
fx
=
f f
( )
Mean=
Freque
ncy
(f)
10
20
30
20
10
f = 90
2=
fx2
180
380
600
420
200
fx =
1780
3240
7220
12000
8820
4000
fx2 =
35280
fx = 1780 =19.78
f 90
2
f x 2 fx
f
f
2
fx
( )
2
35280 1780
2
Example # 02:
Consider following frequency distribution:
Class
Interval
1---5
6---10
11---15
16---20
21---25
frequenc
y
5
10
15
12
8
Class
Interval
(C-I)
1---5
6---10
Frequen
cy
(f)
5
10
Cumulative
frequency
(C.f)
5
15C
Class
Boundary
(C-B)
0.5---5.5
5.5---10.5
11---15
16---20
21---25
Total ()
15f
12
8
f = 50
30
42
50
10.5---15.5
15.5---20.5
20.5---25.5
Median
group
Calculation of Median:
Above frequency distribution is grouped frequency distribution where we have class
intervals so, to find out median use formula to calculate median.
Formula:
[(
Median=l .b +
f C
2
) ( )]
h
f
Where;
f =15 ,C=
15 f
=25
2
[( ) ( ) ]
f
Median=l .b +
Median=10.5+ ( 2515 )
h
f
( 155 )]
Median=10.5+3.33=13.83
Median = 13.83
For Mode:
To find out median we always find median group first.
How to find mode group?
To find out mode group find maximum frequency, where it lies that class would be
our required mode group.
Note: if 2 or more classes have a same maximum frequency then there would be 2
or more mode groups which mean 2 or more mode lies in data subsequently.
Class
Interval
(C-I)
1---5
Frequen
cy
(f)
5
10
f1
15
fm
12
f2
8
6---10
11---15
16---20
21---25
Class Boundary
(C-B)
0.5---5.5
5.5---10.5
10.5---15.5
Mode
group
15.5---20.5
20.5---25.5
Calculation of Mode:
Above frequency distribution is a grouped frequency distribution where we have
class intervals so, to find out mode use formula to calculate mode.
Formula:
M ode=l . b+
[(
f m f 1
h
2 f mf 1f 2
Where;
M ode=l . b+
[(
f m f 1
h
2 f mf 1f 2
Median=10.5+
[(
Median=10.5+
[( ) ]
1510
5
2(15)1012
5
5
8
Mode = 13.625
Mean=
fx
f
variance=
2
fx
fx
=
f f
( )
1---5
6---10
11---15
16---20
21---25
Frequen
cy
(f)
5
10
15
12
8
Total ()
f = 50
Class
Interval
Mean=
2=
fx
fx2
3
8
13
18
23
15
80
195
216
184
45
640
2535
3888
4232
fx2 =
11340
fx = 690
fx = 690 =13. 8
f 50
f x 2 fx
f
f
2
mid point
(x)
( )
1134 0 690 2
2
( )
Mean=13.8 , 2=36.36=6.03