Question

If the mean of observation x,x+3,x+5 , x+7, x+10 is 9, the mean of the last three observation is​

Answer 1

Answer :-

We know that,

$\sf Mean = \dfrac{Sum \: of \: observation}{Total \:number \:of\: observation}$

Here, we are given that mean of 5 terms that are x , x + 3 , x + 5 , x + 7 and x + 10 is 9. So,

$\implies\sf \dfrac{x + x + 3 + x + 5 + x + 7 + x + 10}{5} = 9$

$\implies\sf \dfrac{x + x + x + x + x + 3 + 5 + 7 + 10}{5} = 9$

$\implies\sf \dfrac{5x + 25}{5} = 9$

$\implies\sf 5x + 25 = 9 \times 5$

$\implies\sf 5x + 25 = 45$

$\implies\sf 5x = 45 - 25$

$\implies\sf 5x = 20$

$\implies\sf x = \dfrac{20}{5}$

$\implies\sf x = 4$

Observations = 4 , 4 + 3 , 4 + 5 , 4 + 7 and 4 + 10

Observations = 4 , 7 , 9 , 11 and 14

Now, we have to find mean of last three observations -

Mean of 9 , 11 and 14 =

$\implies\sf \dfrac{9+11+14}{3}$

$\implies\sf \dfrac{34}{3}$

$\boxed{\sf Mean\: of\: last \:three \:observations = \dfrac{34}{3}}$

Answer 2

Step-by-step explanation:

observations=x,x+3,x+5,x+7,x+10

mean =9

mean =sum of observation/no.of observation

mean=x+x+3+x+5+x+7+x+10/5

9=5x+25/5

5x=(5×9)-25

5x=45-25

5x=20

x=20/5

=4

last 3 observation=x+10,x+7,x+5

=14,10,9

mean=14+10+9/3

=33/3

=11

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