Question

If the mean of the observation:x,x+3,x+5,x+7,x+10 is 9, then find the mean of the last three observations.

Answer 1

↬ Given :-

• The mean of the observation x, x+3, x+5, x+7, x+10 is 9.

↬ To find :-

• The mean of last three observation.

↬ Solution :-

we know that,

$\green{\bigstar}\:\:{\underline{\boxed{\bf\pink{Mean=\dfrac{Sum\:of\:observation}{Number\:of\:observation}}}}}$

$\rm\:mean=\dfrac{x+(x+3)+(x+5)+(x+7)+(x+10)}{5}$

$\rm\longrightarrow\:mean=\dfrac{5x+25}{5}$

$\rm\longrightarrow\:mean=\dfrac{\cancel{5}(x+5)}{\cancel{5}}$

$\rm\longrightarrow\:mean=x+5$

Now,

From the above observation,

• Mean = 9 (given)

∴ x + 5 = 9

➝ x = 9 - 5

➝ x = 4

last three observation (x + 5), (x + 7), (x + 10)

➝ (4 + 5), (4 + 7), (4 + 10)

➝ 9, 11, 14

⤤ So, last three observation will be 9, 11, 14

Then,

$\rm\:Mean\:of\:last\:three\:observation=\dfrac{9+11+14}{3}$

$\rm\:Mean\:of\:last\:three\:observation=\dfrac{34}{3}$

$\rm\:Mean\:of\:last\:three\:observation=11\dfrac{1}{3}$

Hence,the mean of last three observation will be 11 ⅓.