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  • I need help with - A data consists of n observations: If and, hten the standard deviation of the data is: - Statistics and Probability - JEE Main

A data consists of n observations:  x_{1},x_{2},........,x_{n}. If \sum_{i=1}^{n}(x_{i}+1)^{2}=9n  and \sum_{i=1}^{n}(x_{i}-1)^{2}=5n, hten the standard deviation of the data is:

  • Option 1)

     

    5

  • Option 2)

     

    \sqrt{7}

  • Option 3)

     

    2

  • Option 4)

     

    \sqrt5

Answers (1)

best_answer

 

Standard Deviation -

In case of discrete frequency distribution 

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

-

 

We have learnt from the concept

\\\sum(x_i + 1)^2 = 9n\;\;\; - (1)\\ \\\sum(x_i - 1)^2 = 5n\;\;\;- (2)\\

(1) + (2)

\\\sum(x_i^2 + 1) = 7n

(1) - (2)

4\sum x_i =4n

\frac{\sum x_i}{n} = 1

\Rightarrow Variance = 6 -1 = 5

SD = \sqrt5


Option 1)

 

5

Option 2)

 

\sqrt{7}

Option 3)

 

2

Option 4)

 

\sqrt5
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