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Can someone explain The mean of a set of 30 observations is 75. If each observation is multiplied by a non-zero number λ and then each of them is decreased by 25, their mean remains the same. Then λ is equal to :

The mean of a set of 30 observations is 75. If each observation is multiplied by a non-zero number λ and then each of them is decreased by 25, their mean remains the same. Then λ is equal to :

  • Option 1)

    \frac{1}{3}

  • Option 2)

    \frac{2}{3}

  • Option 3)

    \frac{4}{3}

  • Option 4)

    \frac{10}{3}

 
Answers (1)
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As we learned

 

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.

-

 

 The new mean = 75\lambda -25

Also we have 

75\lambda -25=75

\Rightarrow \lambda =\frac{4}{3}


Option 1)

\frac{1}{3}

Option 2)

\frac{2}{3}

Option 3)

\frac{4}{3}

Option 4)

\frac{10}{3}

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