Question

If the range and coefficient of range of the data are 20 and 0.2 respectively, then find the largest and smallest values of the data

Answer 1

Range of the data (R) = 20

L – S = 20  ...(1)

Coefficient of range = 0.2

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

0.2 = `20/("L" + "S")`

L + S = `20/0.2`

= `(20 xx 10)/2`

                                       L + S = 100   ...(2)
                                       L − S  = 20    ...(1)
By adding (2) and (1) ⇒ 2L       = 120
                                         L      = `120/2` = 60

substituting the value of L = 60 in (2)

60 + S = 100

S = 100 – 60 = 40

Largest value = 60

Smallest value = 40