Question

If the mean of five observation X, X+1, X+2, X+3 and 14 is 15, then find the value ofx iş
a) 1
b) 6
c) 5
d)8
​

Answer 1

Formula Required :

$\tt Mean = \dfrac{Sum \: of\: Observation }{No \: of \: Observation }$

AnsWer :

x = 13.75

SolutioN :

We have, Formula.

★ Means = Sum of Observation / no of Observation.

15 = x + x + 1 + x + 2 + x + 3 + 14 /5 .

→ 15 = 4x + 20 / 5.

→ 15 * 5 = 4x + 20.

→ 75 = 4x + 20.

→ 75 -20 = 4x.

→ 55 = 4x.

→ x = 55 / 4.

→ x = 13.75.

Therefore, the value of x is 13.75.

Answer 2

Answer:

✩ Given Observations :

⠀ x ,⠀(x + 1) ,⠀(x + 2) ,⠀(x + 3)⠀and⠀14

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf Mean=\dfrac{Sum\:of\:all\: Observations}{Number\:of\: Observations}\\\\\\:\implies\sf15 = \dfrac{x + (x + 1) + (x + 2) +(x + 3) + 14}{5} \\\\\\:\implies\sf 15 \times 5 = 4x + 20\\\\\\:\implies\sf 75 = 4x - 20\\\\\\:\implies\sf 75 - 20 = 4x\\\\\\:\implies\sf 55 = 4x\\\\\\:\implies\sf \dfrac{55}{4} = x\\\\\\:\implies\underline{\boxed{\sf x = 13.75}}$

⠀

$\therefore\:\underline{\textsf{Hence, the required value of x is \textbf{13.75}}}.$

$\rule{150}{1}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Verification

$\dashrightarrow\sf\:\:Mean=\dfrac{Sum\:of\:all\: Observations}{Number\:of\: Observations}\\\\\\\dashrightarrow\sf\:\:15 = \dfrac{x + (x + 1) + (x + 2) +(x + 3) + 14}{5}\\\\\\\dashrightarrow\sf\:\:15 = \dfrac{13.75 + (13.75 + 1) + (13.75 + 2) +(13.75 + 3) + 14}{5}\\\\\\\dashrightarrow\sf\:\:15 = \dfrac{13.75 + 14.75 + 15.75 + 16.75 + 14}{5} \\\\\\\dashrightarrow\sf\:\:15 = \dfrac{75}{5} \\\\\\\dashrightarrow\textsf{ \textbf{15 = 15}}$