Question

Find the range and coefficient of range of the following:

Size of shoes	6	7	8	9	10	11	12	13
No. of shoes sold	8	12	14	20	15	8	7	10

Answer 1

Size of Shoes	No. of Shoes Sold
6	8
7	12
8	14
9	20
10	15
11	8
12	7
13	10

Highest value (H) = 13
Lowest value (L) = 6
Range = Highest value − Lowest value
i.e. R = H − L
or, R = 13 − 6=7
$\mathrm{Coefficient}\mathrm{of}\mathrm{Range}=\frac{H-L}{H+L}=\frac{13-6}{13+6}=\frac{7}{19}=0.368=0.37approx$

Note- As the given data series is a discrete series, where in order to calculate Range, frequencies are not taken into account. Hence, in this case, the formula for Range remains the same as it is for the individual series.