Building a five-number summary and the interquartile range
No formula at all — six numbers read off an ordered list. The whole question is knowing where to cut it, and whether the middle value goes into the halves or stays out.
A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.
ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.
Fourteen students, scores already ordered:
59, 65, 68, 71, 71, 72, 73, 83, 83, 85, 86, 88, 88, 89
What is the median?
Same fourteen scores: 59, 65, 68, 71, 71, 72, 73, 83, 83, 85, 86, 88, 88, 89.
What is the interquartile range?
Seven daily rainfall readings, in millimetres, as recorded:
8, 3, 14, 6, 3, 11, 5
What is the interquartile range?
Nine reaction times, already ordered, in hundredths of a second:
12 15 17 20 22 25 28 31 35
Give the five-number summary and the interquartile range.
The median
The lower quartile
The interquartile range
What happens if you keep the median in
Odd and even lists behave differently
With an odd count the median is a real data value, and it belongs to neither half. That is the rule the practice set exercises, and ignoring it cost 2.5 on the IQR above.
With an even count the median is the average of the two middle values and is usually not in the data at all, so the list splits cleanly and there is nothing to exclude. The exam version has fourteen values, which is the easy case — but you have to notice which one you are looking at before you cut.