Question

You are given the following data: {1, 4, a, 17, 20, b}.

Assuming that a and b are positive integers and ab=18. What is the range?

Range = MaxValue - MinValue

Answer 1

The range of a data set is the difference between the highest value and the lowest value of the data set. That is,

Range = max value - min value

Given the data is, (1, 4 , a, 17, 20, b)

Where a and b are positive integers and ab= 18.

Therefore, we can say a= 9,b=2 or a= 6,b=3 or a=18,b=1 or vice versa (since a and b are positive integers)

When a=9, b = 2, the data set is

(1,4,9,17,20,2)

Range of the data set = 20-1 =19 --------- (i)

When a=6, b= 3, the data set is,

(1,4,6,17,20,3)

Range of the data set = 20-1 = 19 ----------- ( ii )

When a= 18, b = 1, the data set is,

(1,4,18,17,20,1)

Range of the data set = 20-1 = 19 -------------- (iii)

From (i),(ii) , (iii) , we can say, whatever be the value of a and b, such that ab=18, the maximum value is 20 and the minimum value is 1.

Therefore , the range of the data set (1,4,a,17,20,b) is 20-1 = 19 (Ans)