Hi I was solving gregmats third “hard” question quiz and noticed this question:
Greg says that the as set by definition has all unique elements.
Now I was solving a 5LB question:
The answer to this question is D however here is the 5LB explaination:
In most datasets, the range is larger than the interquartile range because the interquartile range ignores the smallest and largest data points. That’s actually the purpose of interquartile range—to get a good picture of where most of the data is (think of the “big hump” on a bell curve). For instance:
Example set A: 1, 2, 3, 4, 5, 6, 7, 100 Here, the range is 100 – 1 = 99.
The interquartile range is Q3 – Q1, or the median of the upper half of the data minus the median of the lower half of the data: 6.5 – 2.5 = 4.
In this example, the range is much larger. However, consider this set:
Example set B: 4, 4, 4, 4, 5, 5, 5, 5
In this set, the range is 5 – 4 = 1. The interquartile range is also 5 – 4 = 1. While the interquartile range can never be greater than the range, they can certainly be equal.
My contention is with the example “set” B. They seem to have allowed duplicate values to illustrate how the IQR and range can be equal. Does this not violate the definition of a set? If not then why are we allowed to consider duplicate values in this question? Is this since the question stem says “datasets” and not “sets”?
Thank you for your help. Greatly appreciate it!