The items produced in a factory are packed into different boxes a… - Vidyadip

Question

The items produced in a factory are packed into different boxes according to their weight. Using the following information, find the range and the relative range of weight of boxes :

Weight (kg)	Oct$-15$	$15-20$	$20-25$	$25-30$	$30-35$
No. of boxes	$8$	$15$	$26$	$47$	$4$

✓

Answer

The given frequency distribution is continuous. The upper limit of the last class and lower limit of the first class will be the highest and lowest observations of the data respectively.
Hence $x_{H}=35$ and $x_{L}=10$
Range $=x_{H}-x_{L}$
$ =35-10$
$=25$
$ \therefore R =25 \mathrm{kgs} .$
Thus, range of the weight of the boxes is $25 \mathrm{kgs}$.
$ \text { Relative range } =\frac{R}{x_{H}+x_{L}} $
$=\frac{25}{35+10} $
$=\frac{25}{45} $
$=0.5556 $
$ \therefore \text { Relative range } =0.56 $
Thus, relative range of the weight of the boxes is $0.56$.

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