Question

If the mean of five observations x,x+2, x+4, x+6, x+8 is 11, find the mean of
first three observations.​

Answer 1

Answer:

Mean of five observations= Sum of all the observations/ Total no.of observations

x+x+2+x+4+x+6+x+8/5= 5x+20/5=11(given)

5x+20=11x5= 5x+20= 55

5x= 55-20

5x= 35

x=7

So,the first three observations are x=7,x+2=7+2=9,x+4=7+4=11

so,their mean = 7+9+11/3= 27 /3 = 9

Hence the answer is 9.........

Answer 2

Answer:

We have,

$\\ \: \: \: \sf11 = \frac{x + (x + 2) + (x + 4) + (x + 6) + (x + 8)}{5} \\ \\ \\ \implies \sf55 = 5x + 20 \\ \\ \\ \implies \sf \: 5x = 35 \\ \\ \\ \implies \sf \blue{x = 7}$

Now, mean of first three observations

$\: \: \sf \: \: \frac{x + (x + 2) + (x + 4)}{3} \\ \\ \\ \implies \sf \frac{3x + 6}{3} = x + 2 \\ \\ \\ \sf \implies 7 + 2 = 9$