Question

if the mean of the observations x, x+3,x+5,x+7 and x+10 is 12. what is the mean of last three observations?​

Answer 1

GiveN:-

If the mean of the observations x, x+3,x+5,x+7 and x+10 is 12.

To FinD:-

Mean of last three observations?

SolutioN:-

We know that,

$\large{\green{\underline{\boxed{\bf{Mean=\dfrac{Sum\:of\:all\:observations}{Total\:no\:of\:observations}}}}}}$

where,

• Total no of observations are 5.
• The observations are:- x, (x + 3), (x + 5), (x + 7), (x + 10).
• Mean = 12.

Putting the values,

$\large\implies{\sf{12=\dfrac{x+x+3+x+5+x+7+x+10}{5}}}$

$\large\implies{\sf{12=\dfrac{5x+25}{5}}}$

$\large\implies{\sf{12\times5=5x+25}}$

$\large\implies{\sf{60=5x+25}}$

$\large\implies{\sf{60-25=5x}}$

$\large\implies{\sf{35=5x}}$

$\large\implies{\sf{\dfrac{35}{5}=x}}$

$\large\implies{\sf{\dfrac{\cancel{35}}{\cancel{5}}=x}}$

$\large\therefore\boxed{\bf{x=7.}}$

The numbers are:-

1. x = 7
2. x + 3 = 7 + 3 = 10
3. x + 5 = 7 + 5 = 12
4. x + 7 = 7 + 7 = 14
5. x + 10 = 7 + 10 = 17

VerificatioN:-

$\large\implies{\sf{12=\dfrac{7+10+12+14+17}{5}}}$

$\large\implies{\sf{12=\dfrac{60}{5}}}$

$\large\implies{\sf{12=\dfrac{\cancel{60}}{\cancel{5}}}}$

$\large\implies{\sf{12=12}}$

$\large\therefore\boxed{\bf{LHS=RHS.}}$

• Hence verified.

Mean of last three observations:-

$\large{\green{\underline{\boxed{\bf{Mean=\dfrac{Sum\:of\:all\:observations}{Total\:no\:of\:observations}}}}}}$

where,

• Total observations = 3.
• The observations are:- 12, 14,17.

Putting the values,

$\large\implies{\sf{Mean=\dfrac{12+14+17}{3}}}$

$\large\implies{\sf{Mean=\dfrac{43}{3}}}$

$\large\therefore\boxed{\bf{Mean=14.3.}}$

Answer 2

Answer:

Given:

x,x+3 ,x+5 ,x+7 and x+10

and mean is 12

To find

mean of the last three observation

SOLUTION

x+x+3+x+5+x+7+x+10 = 12

5

5x+25 = 12

5

5x+25 = 60

5x =35

x =7

the number will be

x = 7

x+3 = 7+3=10

x+5 =7+5 = 12

x +7= 7+7 = 14

x +10 =7+10= 17

Now ,

Find the mean of last three observation

Means = 12+14+17

3

==》mean = 43

3

==》mean= 14.3