Question

Mean of a certain number of observations is . If each observation is divided by m(m ≠ 0) and increased by n, then the mean of new observation is
A. x'/m+n
B. x'/n+m
C. x'+n/m
D.x'+m/n

Answer 1

Given : Mean of a certain number of observations is x(Bar)  . If each observation is divided by m(m ≠ 0) and increased by n.

To find : The mean of new observation .

 

 

Solution :  

we have ,  mean is  x(Bar)

Let x1, x2, …, xk are k observations.

we know that ,  The mean of observations, is the sum of the values of all the observations divided by the total number of observations.

i.e.

x (bar) = (x1+  x2 + x3 + ......+ xk )/k ……….(1)

 

A.T.Q , the terms are divided by m and increased by n. Then  

($\frac{x1}{m}$ + n +  $\frac{x2}{m}$ +n  +$\frac{x3}{m}$ + n  + ......+$\frac{xk}{m}$  + n)

Let the new mean be x

x  = ($\frac{x1}{m}$ + n +  $\frac{x2}{m}$ +n  +$\frac{x3}{m}$ + n  + ......+$\frac{xk}{m}$  + n)/k

 x  = [(x1 +  x2  + x3 + ......+ xk)/m  + kn)]/k

x  = [(x1 +  x2  + x3 + ......+ xk)/mk]  + n

Now, From eq 1 we have

x = x(bar)/m + n

Hence  the mean of new observation is x(bar)/m + n.

The correct option is (A) :  x(bar)/m + n

HOPE THIS ANSWER WILL HELP YOU……

 

Some more questions :  

If the mean of observation x1, x2, ...., xn is x, then the mean of x1 + a, x2 + a, ....., xn + a is

(a)ax

(b)x-a

(c)x+a

(d)xa

https://brainly.in/question/7764455

 

The mean of n observation is x. If the first observation is increased by 1, the second by 2, the third by 3, and so on, then the new mean is

(a)x+2n+1

(b)x+n+1/2

(c)x+n+1

(d)x-n+1/2

https://brainly.in/question/7756202

Answer 2

Step-by-step explanation:

The correct option is (A) : x(bar)/m + n