Box and Whisker Plots

Reading & Creating Box & Whisker Plots

Boxplots

Graphical Representation of the 5-number summary

​Boxplots show the "five number summary" of the data, dividing the data into quarters (25%). From the left to right on the diagram: Minimum, first quartile (Q1), Median (Q2), third quartile (Q3), and maximum. Outliers, if present, are shown as separate dots or asterisks.

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Definitions:

Minimum: The lowest value of the data set

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First Quartile (Q1): ​Middle of the lower half of the data set. 25% of the data lies below this value and 75% lies above.

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Median: Middle of the data set. Half the data (50%) lies below this value and half (50%) lies above. ​

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Third Quartile (Q3): Middle of the upper half of the data set. 75% of the data lies below this value and 25% lies above.​

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Maximum: The highest value of the data set.

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​Two additional pieces of information that can be determined are:

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The Interquartile Range (IQR) = Q3 - Q1

The Range = Max - Min​

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These pieces of information will show the extent to which the data is located near the center or near the extremes of the data set.​

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Measures of Spread

Match

Match the following terms with their definitions

• Minimum (Min)

• First Quartile (Q1)

• Median (Q2)

• Third Quartile (Q3)

• Maximum (Max)

The lowest value of the data set

Middle of the lower half of the data set. 25% of the data lies below this value and 75% lies above.

Middle of the data set. Half the data (50%) lies below this value and half (50%) lies above.

Middle of the upper half of the data set. 75% of the data lies below this value and 25% lies below.

The highest value of the data set

• The lowest value of the data set

• Middle of the lower half of the data set. 25% of the data lies below this value and 75% lies above.

• Middle of the data set. Half the data (50%) lies below this value and half (50%) lies above.

• Middle of the upper half of the data set. 75% of the data lies below this value and 25% lies below.

• The highest value of the data set

Multiple Choice

What do points B and D represent on the box plot?

• Mean and Mode

• Mean and Median

• Least and Greatest Value

• First and Third Quartiles

Multiple Choice

What do points A and E represent on the box plot?

• Mean and Mode

• Mean and Median

• Least and Greatest Value

• First and Third Quartiles

Multiple Choice

What does point C on the box plot represent?

• First Quartile

• Median

• Third Quartile

• Mean

Multiple Choice

What is the median of the data?

• 200

• 100

• 90

• 140

Multiple Choice

What value is the lower quartile?

• 66

• 58

• 60

• 64

Multiple Choice

What data value is the upper quartile (Q3)?

• 64

• 62

• 66

• 58

Multiple Choice

What is the minimum value?

• 64

• 58

• 66

• 60

Multiple Choice

What is the maximum value?

• 64

• 58

• 66

• 60

Multiple Select

What is the minimum and maximum?

• 4

• 12

• 34

• 8

• 11

Multiple Choice

Now lets find the median, what do you do to find it?

• Cross off my numbers in pairs until I get one or two in the middle

• Add all of my numbers together

• Find the most common one

• Subtract the largest and smallest

Multiple Choice

We have two numbers in the center, what do we do to find the median?

• Nothing, we have two medians

• Add them and divide by 2

• We choose the one we like the most

Multiple Choice

What is the interquartile range? (Q3 - Q1)

• 33

• 11

• 26

• 23

Draw

Students in Mrs. Hankins' Algebra class received the following scores on a test:

37 42 48 51 52 53 54 54 55

Find the 5 number summary and create a box and whisker plot for the data.