Question

The mean of 70 observations is 125. If one number is included the new mean is 129. Find the included number.​

Answer 1

       $\text{\huge \bf \underline{Answer:}}$

       $\text{We know that, Mean} = \dfrac{\text{Sum of all observations}}{\text{Number of observations}}$

       $\text{Let the sum of the 70 observations be }S$

$\implies \text{Mean of 70 observations} = \dfrac{S}{70} = 125$

$\implies S = 125 \times 70$

$\implies S = 8750 \text{ ------ (i)}$

       $\text{Let the new number be }x$

$\implies \text{New mean} = \dfrac{S + x}{71} = 129$

$\implies S + x = 129 \times 71$

$\implies S + x = 9159$

       $\text{From (i)}$

$\implies 8750 + x = 9159$

$\implies x = 9159 - 8750$

$\implies x = 409$

  $\therefore \: \: \boxed{\boxed{\text{The includ}\text{ed}\text{ number is }409}}$