Box and Whisker Plots

Box and Whisker Plots

by Siew Leh Koh

Multiple Choice

Which of the films do you think you would not be allowed to legally watch at the cinema?

• Film A

• Film B

• Film C

• Cannot tell

Multiple Choice

How can we tell that the film you would not be allowed to see is film C?

• The minimum value

• The lower quartile

• The upper quartile

• The maximum value

Multiple Choice

Which of the films do you think you would enjoy the most?

• Film A

• Film B

• Film C

• Cannot tell

Multiple Choice

What percentage of film B’s audience were between 15 and 30 (the box)?

• 25%

• 50%

• 75%

• Cannot tell

Multiple Choice

What film would your parents probably enjoy most?

• Film A

• Film B

• Film C

• Cannot tell

Multiple Choice

Which of the following are reasons for why your parents would probably prefer film A?

• Only 25% of the audience was less than 34

• The range is bigger

• It has the greatest maximum age

• The median is greater

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Now we have analyzed these box and whisker plots

• Can you guess what genre of film each box plot might represent?

• Can you work out the target audience of each film?

• Justify your decision using mathematical language

Multiple Choice

In which river are the lengths of the fish more variable?

• River B as the lower quartile is bigger

• River B because it has the minimum length

• River A because the upper quartile is bigger

• River A because the IQR is bigger

Multiple Choice

In which river are the lengths of the fish on average longer?

• River B as the median is bigger

• River B because the lower quartile is bigger

• River A because the upper quartile is bigger

• River A because the maximum value is bigger

​Interpreting the box and whisker plots

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•Easily see lightest / heaviest and range

•The ‘box’ contains the middle 50% of people (the most ‘representative half’)

•The ‘whiskers’ show the lightest 25% and heaviest 25% of people (extremes)

Multiple Select

Which of these comparisons are correct?

• Boys weigh more than girls on average

• The lightest girl is lighter than the lightest boy

• The heaviest boy is the same weight as the heaviest girl

• Girls weight is less consistent than boys

​Comparing Groups 1

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1. ​​“Lightest girl lighter than lightest boy”

2. ​“Heaviest boy heavier than heaviest girl”

3. ​“Most representative half of girls generally lighter than most representative half of boys”

​Comparing Groups 2

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1. ​​“Lightest girl same as lightest boy”

2. ​“Heaviest boy same as heaviest girl”

3. ​“All of the most representative half of girls lighter than most representative half of boys”

4. ​“Three quarters of girls lighter than three quarter of boys”

​Some Terminology

Symmetrical Distribution

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​Some Terminology

​Positive skew: median closer to LQ than UQ

​Some Terminology

​Negative skew: median closer to UQ than LQ