Question

The inerquartile range of 10 , 11 ,12 ,13 ,

Answer 1

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Answer 2

IQR = 2

Explanation:

The first step is to find the median of the data set.

The median is the middle value of the data arranged in ascending order. If there is no middle value then it is the average of the values either side of the middle

10, 11, 12, 13

↑ middle

median =
`(11+12)/(2)` =
`(23)/(2)` = 11.5

The interquartile range ( IQR) is the difference between the upper quartile Q₃ and the lower quartile Q₁

Q₃ is the middle of the data to the right of the median and Q₁ is the middle of the data to the left of the median.

12, 13

↑

Q₃ =
`(12+13)/(2)` =
`(25)/(2)` = 12.5

10, 11

↑

Q₁ =
`(10+11)/(2)` =
`(21)/(2)` = 10.5

Then

IQR = Q₃ - Q₁ = 12.5 - 10.5 = 2