Getting The Best Conclution From Comparing Boxplots (Box-and-Whisker Plots)

The example below shows a comparison of the amount of dirt removed by four brands of detergents (brands A to D).

comparing boxplots

a) Which brand has the biggest range, and what is this range?
A: range =17-10=7
B: range =21-12=9
C: range =22-15=7
D: range =18-11=7
B has the biggest range. The range is 9.
b) For brand C, what does the number 18 mg represent?
18 mg represents the median.
c) Give the interquartile range for brand B.
interquartile range =Q3Q1

d) Which brand of detergent would you buy? Explain your answer.
We need to compare several values to help us decide. These values are shown in the table below.

From this we see that brand C has the highest minimum value. Brand B has the smallest interquartile range but the largest range. It is possible that the minimum value for brand B is an outlier which would make brand B a better choice than brand C.
Considering all the data available it would be hard to choose between brand C and brand B. We can however say that brands A and D are not very good choices as they both have low minimum and maximum values.
Since brand C does not have a potential outlier this might be the best brand to choose.
Let’s read the post ‘Drawing Box-and-Whisker Plots (Boxplots)‘.

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