Question

13. (a) Find SD from the following

Items : 5 15 25 35 40

Frequency : 5 8 15 16 6​

Answer 1

%%2245anddgfihbffjdkdnjdkdkdkd

Answer 2

Answer:

Class interval f

i

x

i

u

i

=

h

x

i

−A

u

i

2

f

i

u

i

f

i

u

i

2

0-10 5 5 -2 4 -10 20

10-20 8 15 -1 1 -8 8

20-30 15 25 0 0 0 0

30-40 16 35 1 1 16 16

40-50 6 45 2 4 12 24

Total 50 10 68

We have N=∑f

i

=50

Width of class h=10

Assumed mean A=25(say)

Mean,

x

ˉ

=A+

N

∑

i=1

5

f

i

u

i

×h

=25+

50

10

×10=25+2=27

⇒

x

ˉ

=27

Variance σ

2

=h

2

⎣

⎢

⎡

N

∑

i=1

5

f

i

u

i

2

−(

N

∑

i=1

5

f

i

u

i

)

2

⎦

⎥

⎤

σ

2

=10

2

⎣

⎢

⎡

50

68

−(

50

10

)

2

⎦

⎥

⎤

=10

2

(50)

2

[50×68−(10)

2

]

=

25

1

[3400−100]

=

25

3300

=132