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  • Can someone explain The mean and the standard deviation(s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :

The mean and the standard deviation(s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :

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Answers (1)

best_answer

As we have learned

Standard Deviation -

If x1, x2...xn are n observations then square root of the arithmetic mean of 

\sigma = \sqrt{\frac{\sum \left ( x_{i}-\bar{x} \right )^{2}}{n}}

\bar{}

- wherein

where \bar{x} is mean

 

 

ARITHMETIC Mean -

For the values x1, x2, ....xn of the variant x the arithmetic mean is given by 

\bar{x}= \frac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n}

in case of discrete data.

-

 

since sd = 0

mean = 9

  thus all observations are =9 

now mean = 10

\frac{9+9+9+9+x}{5}=10

x=14 

so sd =  \sqrt\frac{(9-10)^{2}+(9-10)^{2}+.....+(14-10)^{2}}{5}=2

 

 

 

 

 

 

 


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Posted by

Himanshu

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