Question

please help to solve this type of question...

Need step by step explanation how to solve such mcqs ​

Answer 1

Correct Question

If the mean of the observations x, x+3, x+5, x+7 and x+10 is 9. The mean of last three observations is

$\sf (a) \dfrac{31}{3}$

$\sf (b) \dfrac{32}{3}$

$\sf (c) \dfrac{34}{3}$

$\sf (d) \dfrac{35}{3}$

Answer

$\sf \dashrightarrow Mean = \dfrac{Sum \: of \: all \: observations}{Number \: of \: observations}$

$\sf \dashrightarrow 9 = \dfrac{x + (x + 3) + (x + 5) + (x + 7) + (x + 10)}{5}$

$\sf \dashrightarrow 9 = \dfrac{5x + 8 + 17}{5}$

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

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

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

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

$\sf \dashrightarrow 5x = 20$

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

$\sf \dashrightarrow x = 4$

Now, we should find the values of a

last three observations.

Value of third observation :

$\sf \dashrightarrow x + 5$

$\sf \dashrightarrow 4 + 5$

$\sf \dashrightarrow 9$

Value of fourth observation :

$\sf \dashrightarrow x + 7$

$\sf \dashrightarrow 4 + 7$

$\sf \dashrightarrow 11$

Value of fifth observation :

$\sf \dashrightarrow x + 10$

$\sf \dashrightarrow 4 + 10$

$\sf \dashrightarrow 14$

Now, we can find the mean of all these numbers.

$\sf \dashrightarrow \dfrac{(x + 5 + (x + 7) + (x + 10)}{3}$

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

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

Hence, the mean of the last three observations is $\sf \dfrac{34}{3}$

Thus, Option(C) is the right answer.