Question

Mean of 12 observations is 17. if each observation is decreased by 2, find the new mean.

Answer 1

We know that mean of (x~)=(x1+x2+x3+x4-.......)÷n Where (n) is number of frequency.. Then {(17×12)+(12×2)}÷12=(12×19)÷12=19

Answer 2

Answer:

15

Step-by-step explanation:

Let the 12 observations be : $x_1,x_2,x_3.....,x_{12}$

We are given that Mean of 12 observations is 17

So, $Mean = \frac{\text{Sum of all observations}}{\text{total no. of observations}}$

$12= \frac{x_1+x_2+x_3+....+x_{12}}{17}$

$12 \times 17= x_1+x_2+x_3.....+x_{12}$

$204= x_1+x_2+x_3+....+x_{12}$ --1

Now we are given that each observation is decreased by 2,

So,  $\text{New Sum} = x_1-2+x_2-2+x_3-2+...+,x_{12}-2$

$\text{New Sum} = (x_1+x_2+x_3+....+x_{12})-(2\times 12)$

Using 1

$\text{New Sum} = 204 -24$

$\text{New Sum} =180$

So, New Mean = $\frac{180}{12}$

New Mean = $15$

Hence the new mean is 15