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

Draw

Order the numbers from least to greatest. (Make sure to write these down to refer back to)

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

Fill in the Blank

What is the median? (Your numbers were 15 & 17)

Fill in the Blank

What do you think is the lower quartile?

Fill in the Blank

What do you think is the upper quartile?

Multiple Choice

What is the interquartile range? (Q3 - Q1)

• 33

• 11

• 26

• 23

Draw

Students in Mrs. Ramon's 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.