Question

The mean of p numbens is 48. The
mean of anothers q numbers is 51.
Express, as a single fraction, the
mean of p+q numberos.​

Answer 1

$\textbf{Given:}$

$\text{Mean of p numbers is 48}$

$\text{Mean of q numbers is 51}$

$\textbf{To find:}$

$\text{The mean of p+q numbers}$

$\textbf{Solution:}$

$\text{Since mean of p numbers is 48,}$

$\text{Mean of p numbers}=\dfrac{\text{Sum of p numbers}}{p}$

$48=\dfrac{\text{Sum of p numbers}}{p}$

$\text{Sum of p numbers}=48\,p$

$\text{Sum of q numbers}=51\,q$

$\text{Using combined mean formula}$

$\text{Combined mean}=\dfrac{n_1\,\bar{x_1}+n_2\,\bar{x_2}}{n_1+n_2}$

$\implies\text{Combined mean}=\dfrac{p(48)+q(51)}{p+q}$

$\implies\bf\text{Combined mean}=\dfrac{48\,p+51\,q}{p+q}$

$\therefore\textbf{The mean of p+q numbers is \bf\dfrac{48\,p+51\,q}{p+q} }$

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