Question

2. (a) The mean and standard deviation of one sample are respectively 54.4 and 8; the mean and standard deviation of another sample are 50.3 and 7 respectively The size of the first sample is 50 and that of second is 100. Find the standard deviation of the composite sample combining the aforesaid two samples.​

Answer 1

Answer:

Correct option is

A

7.56

n

1

=50 & n

2

=100.

x

ˉ

1

=54.1 &

x

ˉ

2

=50.3.

σ

1

=8 & σ

2

=7.

x

ˉ

=

n

1

+n

2

n

1

x

ˉ

1

+n

2

x

ˉ

2

=

150

50×54.1+100×50.3

=51.567.

σ

1

=

x

ˉ

1

−

x

ˉ

=54.1−51.56=2.53.

σ

2

=

x

ˉ

2

−

x

ˉ

=50.3−51.56=−1.26.

σ

2

(n

1

+n

2

)=n

1

(σ

1

2

+d

1

2

)+n

2

(σ

2

2

+d

2

2

)=50(60+6.4)+100(49+1.58)

σ

2

(150)=3520+5058

σ

2

=

150

8578

=57.18

σ=7.56

Answer 2

Answer:

Mean 51.6 (approx)

STD dev 7.3 (approx)

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