PROBLEMS ON RANGE AND COEFFICIENT OF RANGE

The difference between the largest value and the smallest value is called Range.

Range R = L – S

Coefficient of range = (L - S)/(L + S)

where L - Large value; S - Small value

Question 1 :

Find the range and coefficient of range of the following data

(i) 59, 46, 30, 23, 27, 40, 52, 35, 29

(ii) 41.2, 33.7, 29.1, 34.5, 25.7, 24.8, 56.5, 12.5

Solution :

Range (R)  =  L–S

=  59 – 23

=  36

Coefficient of range  =  (L–S)/(L+S)

=  (59–23)/(59+23)

=  36/82

=  0.4390

=  0.44

(ii) 41.2, 33.7, 29.1, 34.5, 25.7, 24.8, 56.5, 12.5

Solution :

Range (R)  = L–S

R  =  56.5–12.5

=  44

Coefficient of range  =  (L–S)/(L+S)

=  (56.5–12.5)/(56.5+12.5)

=  44/69

=  0.6376

=  0.64

Question 2 :

The smallest value of a collection of data is 12 and the range is 59. Find the largest value of the collection of data.

Solution :

S  =  12, R  =  59

R  =  L–S

59  =  L–12

L  =  59+12

L  =  71

So, the largest value is 71.

Question 3 :

The largest of 50 measurements is 3.84 kg. If the range  is 0.46 kg, find the smallest measurement. 

Solution :

L  =  3.84, R  =  0.46

R  =  L–S

0.46  =  3.84–S

S = 3.84 – 0.46

S = 3.38 kg

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