Question

c) If the mean of the observations p, p+2, p+4, p+6 and p +8 is 11, then find :


i)the mean of first three observations.​

Answer 1

mean of 5 observations is equals to 11

mean = (p+p+2 +p+4+p+6+p+8 ) / 5

11 = (5p + 20) /5

55= 5p +20

55-20 = 5p

35= 5p

35/5 = p

7=p

Now observations are ; 7,9,11,13,15.

So mean of First 3 observations = 7+9+11/3

mean = 27/3 = 9

Answer 2

Answer:

The required mean of first three observations is 9

Step-by-step explanation:

Given :

The mean of the observations p, p+2, p+4, p+6 and p +8 is 11

To find :

The mean of first three observations

Solution :

$\boxed{\longrightarrow \sf Mean=\dfrac{Sum \ of \ observations}{number \ of \ observations}}$

First, let's find the value of p.

   $\sf 11=\dfrac{p+p+2+p+4+p+6+p+8}{5} \\\\ \sf 11=\dfrac{5p+20}{5} \\\\ \sf 11 \times 5=5p+20 \\\\ \sf 55=5p+20 \\\\ \sf 55-20=5p \\\\ \sf 5p=35 \\\\ \sf p=35/5 \\\\ \sf p=7$

Substitute the value of p,

The observations are :-

• p = 7
• p + 2 = 7 + 2 = 9
• p + 4 = 7 + 4 = 11
• p + 6 = 7 + 6 = 13
• p + 8 = 7 + 8 = 15

We have to find the mean of first three observations.

   The first three observations are 7 , 9 and 11

   $\sf Mean=\dfrac{7+9+11}{3} \\\\ \sf Mean=\dfrac{27}{3} \\\\ \sf Mean=9$

Therefore, the mean of first three observations is 9