If the standard deviation of the numbers 2, 3, a and 11 is 3.5,

then which of the following is true ?

  • Option 1)

    3a2 − 26 a + 55 = 0

     

  • Option 2)

     3a2 − 32a + 84 = 0

     

  • Option 3)

    3a2 − 34a + 91 = 0

     

  • Option 4)

    3a2 − 23a + 44 = 0

     

 

Answers (1)

As we learnt in

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

 

 

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

\Rightarrow \frac{49}{4}=\frac{4+9+a^{2}+121}{4}\:-\left (\frac{16+a}{4} \right )^{2}

\Rightarrow 3a^{2}-32a+84=0

   


Option 1)

3a2 − 26 a + 55 = 0

 

This option is incorrect.

Option 2)

 3a2 − 32a + 84 = 0

 

This option is correct.

Option 3)

3a2 − 34a + 91 = 0

 

This option is incorrect.

Option 4)

3a2 − 23a + 44 = 0

 

This option is incorrect.

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