Question

Kelly found the interquartile range for the data: 7, 11, 12, 16, 18, 22, 24, 30. She found the median is 17, the lower quartile is 11, the upper quartile is 24, and the interquartile range is 13. Is her calculation of the interquartile range correct? Explain your answer.

Answer 1

Kelly found the incorrect quartiles. She should have included 16 in the bottom half of the data and 18 in the top half of the data. If she had, she would have found the interquartile range to be 11.5.

Answer 2

Kelly made an error in the calculation of IQR

Explanation:

We can recheck the calculations to find if her calculation was correct or not.

So,

The data is:

7, 11, 12, 16, 18, 22, 24, 30

The median will be the average of middle two values as the number of values is even.

Median = (16+18)/2

= 34/2

=17

17 divides data in two equal parts.

So,

for Q1, our data is:

7,11,12,16

The first quartile will be the average of middle two values .

Q1 = (11+12)/2

= 23/2

= 11.5

For Q3:

18,22,24,30

Q3 = (22+24)/2

= 46/2

= 23

So

IQR = Q3-Q1

= 23 - 11.5

= 11.5

So Kelly's calculation of interquartile range was incorrect because she made a mistake in finding Q1 and Q3 ..