Question

The least value of items in a distribution in 65 and the range is 30. what is the largest size of the items and coefficient of range?
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Answer 1

Answer:

Given

Coefficient of range = 0.5

Smallest value = S = 12

Formula

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

L = Largest value

S = Smallest value

Calculation

Let the largest value be x

⇒ 0.5 = (x - 12)/(x + 12)

⇒ 0.5(x + 12) = (x - 12)

⇒ 0.5x + 6 = x - 12

⇒ 0.5x = 18

⇒ x = 36

∴ The value of Largest number is 36

Important Points

Range is the simplest measure of dispersion. We can define range as the difference between the highest and the lowest value in a set of observation

For example the range of the series 1, 2, 4, 6, 8, 9, 10, 12

Largest number = 12

Lowest number = 1

Range = L - S = 12 - 1 = 11

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

Coefficient of this range = 11/13