Question

In a retail market , fruit vendors were selling mangoes kept in packed boxes. These boxes contained different number of mangoes. The following was the distribution of mangoes according to the number of boxes ?

Number of mangoes	$50-52$	$53-55$	$56-58$	$59-61$	$62-64$
Number of boxes	$15$	$110$	$135$	$115$	$25$

Find the mean number of mangoes using step-deviation method.

Answer 1

No of mangoes	No of boxes $\left(F_i\right)$	Class mark $\left(x_i\right)$	$X_i-A$	$Ui=\frac{Xi-A}{h}$	$FiUi$
$50-52$	$15$	$51$	$-6$	$-2$	$-30$
$53-55$	$110$	$54$	$-3$	$-1$	$-110$
$56-58$	$135$	$57$	$0$	$0$	$0$
$59-61$	$115$	$60$	$3$	$1$	$115$
$62-64$	$25$	$63$	$6$	$2$	$50$
	$\sum Fi=400$				$\sum FiUi=25$

$mean,\left(\stackrel{-}{x}\right)=A+h\times \frac{\sum F_i{U}_i}{\sum F_i}$

$where,A=assumedmean=57h=classsize=3$

$\sum F_i=400$

$\sum F_i{U}_i=25$

$mean\left(\stackrel{-}{x}\right)=A+h\times \frac{\sum F_i{U}_i}{\sum F_i}$

$mean\left(\stackrel{-}{x}\right)=57+3\times \frac{25}{400}$

$=57+0.1875$

$=57.1875$

Hence, the mean number of mangoes in each box is $57.1875$ .