Question

SECTION C EACH HAVING 3
Q.17 The mean of five numbers is 27. If one more number is included, then the mean is 26. Find the
included number.​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

$\tt \: Let \: the \: five \: observations \: be \: x_1, x_2, x_3, x_4, x_5$

$\tt \:  Mean \: of \: 5 \: observation \: is \: 27$

$\tt \:  Using \: Formula$

$\bf \:Mean = \dfrac{Sum \: of \: observations}{Number \: of \: observations }$

$\tt \:  \longrightarrow \: 27 = \dfrac{x_1 + x_2 + x_3 + x_4 + x_5}{5}$

$\tt \:  \longrightarrow \: x_1 + x_2 + x_3 + x_4 + x_5 = 27 \times 5$

$\tt \:  \longrightarrow \: x_1 + x_2 + x_3 + x_4 + x_5 = 135 - - - (i)$

$\tt \:  \boxed{ \purple{\tt \:  Let \: the \: included \: number \: be \: x_6}}$

$\begin{gathered}\bf\red{According \: to \: statement}\end{gathered}$

$\tt \:  \longrightarrow \: Mean \: of \: 6 \: observation \: is \: 26.$

$\tt \:  \longrightarrow \: Using \: Formula$

$\bf \:Mean = \dfrac{Sum \: of \: observations}{Number \: of \: observations }$

$\tt \:  \longrightarrow \: 26 = \dfrac{x_1 + x_2 + x_3 + x_4 + x_5 + x_6}{6}$

$\tt \:  \longrightarrow \: x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 6 \times 26$

$\tt \:  \longrightarrow \: 135 + x_6 = 156$

$\tt\implies \: \large \boxed{ \purple{\tt \: x_6 = 21 }}$