Question

f the mean of the observations: x, x + 3, x + 5, x + 7, x + 10 is 9,Find the mean of the last three observations.​

Answer 1

Step-by-step explanation:

Mean of x,x+3,x+5,x+7,x+10=9

Sum of the terms =5x+25

Mean =

5

5x+25

=9

x+5=9

x=4

Last three observations are 9,11,14

Mean =

3

9+11+14

=11

3

1

Answer 2

$\dag \: \underline{\sf AnsWer :}$

• We are given that, the mean of the observations as x, x + 3, x + 5, x + 7, x + 10 is 9. Total number of observation = 5 and we need to find the mean of the last three observations.

$\bigstar\: \underline{\textbf{According to the Question Now :}}$

$:\implies\sf Mean = \dfrac{Sum \: of \: total \: observation}{Total \: number \: of \: observation}$

$:\implies\sf 9 = \dfrac{x + x + 3 + x + 5 + x + 7 + x + 10}{5}$

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

$:\implies\sf 9 \times 5= 5x +25$

$:\implies\sf 45= 5x +25$

$:\implies\sf 45 - 25= 5x$

$:\implies\sf 20= 5x$

$:\implies\sf x = \dfrac{20}{5}$

$:\implies \underline{ \boxed{\sf x =4 }}$

$\bigstar\: \underline{\textbf{Last three observation's :}}$

$\bullet\:\textsf{x + 5 = 4 + 5 = \textbf{9}}$

$\bullet\:\textsf{x + 7 = 4 + 7 = \textbf{11}}$

$\bullet\:\textsf{x + 10= 4 + 10 = \textbf{14}}$

$\bigstar\: \underline{\textbf{The mean of last three observation's :}}$

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

$\dashrightarrow\:\:\sf Mean = \dfrac{34}{3}$

$\dashrightarrow\:\: \underline{ \boxed{\sf Mean = 11\dfrac{1}{3}}}$