Question

The table given below gives the pocket money that 30 students get. Find the mean pocket money.

Pocket money$\left( \text{in Rs} \right)$	3000	4000	5000	6000
Number of students	12	6	8	4

Answer 1

Hint: An arithmetic mean is calculated by adding several \[quantities\] together and dividing the sum by the number of quantities.
Say, we have given \[5\text{ }quantities\] \[a,b,c,d,e\] . Then there arithmetic mean is given by expression:
$Mean=\dfrac{a+b+c+d+e}{5}$
In this question, we have given the frequency of each quantity \[\left( \text{say }{{f}_{i}} \right)\]. So first multiply this frequency by the quantity value $\left( \text{say }{{x}_{i}} \right)$ And then sum is calculated of all these products, given by expression,
$\sum {{x}_{i}}{{f}_{i}}$
Thus mean is given by expression,
\[Mean=\dfrac{\sum {{x}_{i}}{{f}_{i}}}{{{f}_{i}}}\]
Formula used:
$Mean=\dfrac{\text{sum of quantities}}{\text{No of quantities}}=\dfrac{\sum {{x}_{i}}{{f}_{i}}}{\sum {{f}_{i}}}$

Complete step-by-step answer:
$\text{Total no of students given=}30$
$12\text{ students received Rs }3000$
 $\begin{align}
  & \Rightarrow \text{Total money}=12\times \text{Rs }3000 \\
 & \text{ =Rs }36000 \\
\end{align}$
$6\text{ students received Rs }4000$
  $\begin{align}
  & \Rightarrow \text{Total money }=6\times \text{Rs }4000 \\
 & \text{ }=\text{Rs }24000 \\
\end{align}$
$8\text{ students received Rs }5000$
 $\begin{align}
  & \Rightarrow \text{Total money}=8\times \text{Rs }5000 \\
 & \text{ }=\text{Rs 40000} \\
\end{align}$
$4\text{ students received Rs }6000$
$\begin{align}
  & \Rightarrow \text{Total money}=4\times \text{Rs }6000 \\
 & \text{ }=\text{Rs }24000 \\
\end{align}$
 $\begin{align}
  & \text{Sum of all quantities}=36000+24000+40000+24000 \\
 & \text{ }=124000 \\
 & \text{Total no of student }=30 \\
 & Mean\text{ pocket money received}=\dfrac{124000}{30} \\
 & \text{ }=\text{Rs }4133\cdot 33 \\
\end{align}$

Note:Students can solve the sum directly in tabular form as:

\[{{x}_{i}}\left( {{f}_{i}} \right)\]	${{f}_{i}}$	${{f}_{i}}{{x}_{i}}\left( \text{Rs} \right)$
$3000$	$12$	$36000$
$4000$	$6$	$24000$
$5000$	$8$	$40000$
$6000$	$4$	$24000$
	$\sum {{f}_{i}}=30$	$\sum {{f}_{i}}{{x}_{i}}=124000$

$\begin{align}
  & \Rightarrow Mean\text{ pocket money}=\dfrac{124000}{30} \\
 & \text{ =Rs }4133\cdot 33 \\
\end{align}$
In such types of questions, remember to write $unit$ in the value answered. $\left( \text{Here we have write }Rupee,\text{ there can be }m,g,l\text{ etc} \right)$ .Ignore if nothing is mentioned.