Q

# 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)

$\frac{10}{3}$

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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

$\dpi{100} \bar{x}= \frac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n}$

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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