We have done with individual series (Ungrouped data)---here we had no frequency, no class

Now we will do for grouped data .....

1) Discrete Series(Frequency)

2) Continuous Series(frequency and class)

1)Discrete series:- In this series, there are frequency corresponding to different values of the

variable.

HERE Again we have same 3 methods :-

1)Direct Method

2)Short cut method

3)Step deviation method

DIRECT METHOD

Marks 10 20 30 40 50

No. of students

15 10 40 20 15

Here Marks=X

And No of students= frequency(f)

Now direct method

Mean=ΣfX/ Σf

Here ΣfX=150+200+1200+800+750=3100

Σf=15+10+40+20+15=100

Mean= 3100/100=31

SHORTCUT METHOD

Mean(X’)=A+ Σfd/ Σf

Marks(X) No. of students(f) d=X-A(here A=30) fd

10 15 -20 -300

20 10 -10 -100

30(Assumed mean) 40 0 0

40 20 10 200

50 15 20 300

Σf=100 Σfd=100

Mean= 30+100/100=31

STEP DEVIATION METHOD

Draw the same above table

Marks(X) No. of students(f) d=X-A(here A=30)

d’=d/c (c=common factor) c=10

Fd’

10 15 -20 -2 -30

20 10 -10 -1 -10

30(Assumed mean) 40 0 0 0

40 20 10 1 20

50 15 20 2 30

Σf=100 Σfd=10

C=common factor.....u can take anything..but take such that it will be divisible with all the d ...for

easy calculations

Mean= A+ Σfd’/ Σf * c

=30+10/100 *10 =31

CONTINUOUS SERIES

In this series , we have class and frequency both.

continuous means it contains range .....suppose 1-5, 2-10,......

Again same 3 methods will be used

1)DIRECT METHOD

Marks 0-4 4-8 8-12 12-16 16-20

No. of students

4 8 2 1 5

Mean= Σfm/ Σf

Here m= middle no.

m=(first no. +last no.)/2

Marks(X) No. of students(f) Middle no(m) fm

0-4 4 2 8

4-8 8 6 48

8-12 2 10 20

12-16 1 14 14

16-20 5 18 90

Σf=20

Σfm=180

Mean=180/20=9

SHORTCUT METHOD

Marks(X) No. of students(f) Middle no(m) d=m-A fd

0-4 4 2 -8 -32

4-8 8 6 -4 -32

8-12 2 10(Assumed mean=A) 0 0

12-16 1 14 4 4

16-20 5 18 8 40

Σf=20

Σfd=-20

Mean(X’)=A+ Σfd/ Σf

=10+(-20/20)=9

STEP DEVIATION METHOD

Marks(X) No. of students(f) Middle no(m) d=m-A

d’=d/c (let c=4)

Fd’

0-4 4 2 -8 -2 -8

4-8 8 6 -4 -1 -8

8-12 2 10(Assumed mean=A) 0 0 0

12-16 1 14 4 1 1

16-20 5 18 8 2 10

Σf=20

Σfd’=-5

Mean(X’)=A+ Σfd’/ Σf *c

=10+(-5/20) *4=9