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  • Try this! A sample of 35 observation has the mean 30 and SD as 4. A second sample of 65 observations from the same population has mean 70 and SD as 3. The SD of the combined sample is

A sample of 35 observation has the mean 30 and SD as 4. A second sample of 65 observations from the same population has mean 70 and SD as 3. The SD of the combined sample is

  • Option 1)

    5.85

  • Option 2)

    5.58

  • Option 3)

    3.42

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we learned

 

Properties of Standard deviation -

Let n1 , n2 be the number of observations of two series and their means and S.D are \bar{x_{1}},\bar{x_{2}} and \sigma _{1},\sigma _{2} respectively.

Let \bar{x} denote the combined mean of two series then 

\bar{x}= \frac{n_{1}\bar{x_{1}}+n_{2}\bar{x_{2}}}{n_{1}+n_{2}}

\therefore The combined variance of two series is given by 

\sigma ^{2}= \frac{n_{1}\left ( \sigma _{1}^{2}+d_{1}^{2} \right )+n_{2}\left ( \sigma _{2}^{2}+d_{2}^{2} \right )}{n_{1}+n_{2}}

 

 

- wherein

where 

\dpi{100} d_{1}=\bar{x_{1}}-\bar{x}   and   d_{2}=\bar{x_{2}}-\bar{x}

 

 Her  n1=35,\bar{x}_{1}=30,\sigma _{1}=4,n_{2}=65,\bar{x}_{2}=70,\sigma^{2}=3

\therefore\bar{x}_{12}=\frac{35\times 30+65\times 70}{35+65}=73.5

\therefore\bar{x}_{12}=\sqrt{\frac{35(16+42\times 25)+65(9+12\times25)}{100}}

=\sqrt{34.21}=5.85

 


Option 1)

5.85

Option 2)

5.58

Option 3)

3.42

Option 4)

none of these

Posted by

Himanshu

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