The Interquartile Range.

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Presentation transcript:

The Interquartile Range. Menu

What if there is an extra number ? Interquartile Range. What if there is an extra number ? Interquartile Range = Upper Quartile – Lower Quartile. 23 47 12 46 22 58 35 68 10 14 Median = 29 70 U.Q. = Q3= 47 L.Q.=Q1 = 14 Interquartile Range = 47 – 14 = 33 10 12 14 22 23 35 46 47 58 68 Median = 35 L.Q. = 14 U.Q. = 58 Interquartile Range = 58 – 14 = 44 Menu

Why use the Interquartile Range ? Menu

Monica’s exam marks : 88 %, 90 %, 89%, 91%, 92%, 93%, 89%, 90% This small Interquartile Range shows that Mark is consistent. A small Interquartile Range also shows that the Middle half of the numbers are bunched together. Range = 93 – 88 = 5% (Small Range) A Small Range means that Monica is very consistent, predictable, reliable. Marco’s exam marks : 92% 88% 89% 91% 94% Why do we bother with the Interquartile Range ? Why don’t we simply use the Range all of the time ? Range = 94 – 32 = 62% (Big Range) 90% 92% 32% A Big Range means that Marco is very inconsistent, unpredictable, unreliable. But Marco is predictable ! It was only the 32% that gave the impression that he is inconsistent ! I will try the Interquartile Range ! L.Q. = 88.5 U.Q. = 92 Median = 90.5 Interquartile Range = 92 – 88.5 = 3.5 (Small Interquartile Range) Menu

It all depends what do you need to use the data for: Range vs. IQR Rank students in a class Show students ability to master statistics Show what is the student performance in general. Compare two students overall performance Understand what topic may be challenging for students Find causes of variation