Question

the mean of a,b,c and d is 9 and the mean of a,b,c,d,eand f is 12.find the mean of e and f. right ans is 18.​

Answer 1

Answer:

a+b+c/4=9

a+b+c+d=36

a+b+c+d+e+f/6=12

36+e+f=72

e+f=72-36

e+f=36

Answer 2

Answer :-

Mean of e and f = 18

Solution :-

First of all, we should know the formula of mean as the whole question is based on mean.

$\boxed{Mean=\dfrac{Sum\:\:of\:\:all\:\:observations}{Total\:\:no.\:\:of\:\:observations} }$

In the question, the first information given to us is the mean of a, b, c and d is 9.

Here,

Sum of all observations = a + b + c + d

Total no. of observations = 4

So,

=> Mean of a, b, c and d = $\dfrac{a + b + c + d}{4}$

=> 9 = $\dfrac{a + b + c + d}{4}$

=> 9 × 4 = a + b + c + d

=> 36 = a + b + c + d   ....eq. i.)

Second information given to us is the mean of a, b, c, d, e and f is 12.

Here,

Sum of all observations = a + b + c + d + e + f

Total no. of observations = 6

So,

=> Mean of a, b, c, d, e and f = $\dfrac{a + b + c + d+e+f}{6}$

=> 12 = $\dfrac{a + b + c + d+e+f}{6}$

=> 12 × 6 = a + b + c + d + e + f

=> 72 = a + b + c + d + e + f

Substituting the value of a + b + c + d from eq. i.) which is 36.

=> 72 = 36 + e + f

=> 72 - 36 = e + f

=> 36 = e + f    ....eq. ii.)

Now, it is said in the question to find the mean of e and f. So,

Sum of all observations = e + f

Total no. of observations = 2

=> Mean of e and f = $\dfrac{e+f}{2}$

Substituting the value of e + f from eq. ii.) which is 36.

=> Mean of e and f = $\dfrac{36}{2}$

=> Mean of e and f = 18.