Question

What is the interquartile range for this data set?​

Answer 1

The inter-quartile range is 12

Step-by-step explanation

The given data set is

`12, x,x+6,30`

If the median is 17, then

`(x + x + 6)/(2) = 17`

`2x + 6 = 2 * 17`

`2x + 6= 34`

`2x = 34 - 6`

`2x = 28`

`x = 14`

Hence , the data set becomes,

`12, 14,20,30`

The lower quartile is

`Q_1 = (12 +14 )/(2) = 13`

The upper quartile is

`Q_3 = (20 + 30)/(2) = 25`

The inter-quartile range is

`Q_3 - Q_1 = 25 - 13 = 12`