Question

Which statement is the most appropriate comparison of the spreads?A. The standard deviation for town A, 20", is greater than thestandard deviation for town B, 10°.B. The interquartile ranges (IQRs) for towns A and B are both 20°.C. The interquartile range (IQR) for town A, 30°, is less than the IQRfor town B, 46".D. The interquartile range (IQR) for town A, 20", is greater than theIQR for town B, 10".

Answer 1

We are given two box plots of a variable, for two different towns. Recall that the structure of a box plot is

where Q1 is the 25th percentile (or quartile 1), Q2 is the median and Q3 is the 75th percentile (or Quartile 3). This type of graphs tells us how the data is distributed, and more specially it can tell us how the data is spread across the different values the variable could take. So the way to analyze the spread from the graph is by considering the inter quartile range (IQR). This amount can be calculated by simply finding the difference between Q3 and Q1. If this range is really small, this would mean that the data is less spread and if this range is big, then this would mean that the data is more spread.

Using the given box plots, we can determine the following:

Town A: Q3 = 40, Q1 = 20, IQR = 40-20=20

Town B: Q3 = 45, Q1=35, IQR = 45-35 = 10

So, this would lead to option D.