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Box-and-Whisker PlotsBox-and-Whisker Plots

Median, Quartiles, Inter-Quartile Range and Box Plots.

Measures of SpreadThe range is not a good measure of spread because one extreme, (very high or very low value) can have a big affect. The measure of spread that goes with the median is called the inter-quartile range and is generally a better measure of spread because it is not affected by extreme values.

A reminder about the median

1. Order the set of numbers from least to greatest1. Order the set of numbers from least to greatest

Step 1 – Order NumbersStep 1 – Order Numbers

2. Find the 2. Find the medianmedian. The median is the middle . The median is the middle number. If the data has two middle numbers, number. If the data has two middle numbers, find the mean of the two numbers. What is the find the mean of the two numbers. What is the median?median?

Step 2 – Find the MedianStep 2 – Find the Median

3. Find the 3. Find the lower and upper medians or lower and upper medians or quartilesquartiles. These are the middle numbers on . These are the middle numbers on each side of the median. What are they?each side of the median. What are they?

Step 3 – Upper & Lower QuartilesStep 3 – Upper & Lower Quartiles

Now you are ready to construct Now you are ready to construct the actual box & whisker graph. the actual box & whisker graph. First you will need to draw an First you will need to draw an ordinary number line that ordinary number line that extends far enough in both extends far enough in both directions to include all the directions to include all the numbers in your data:numbers in your data:

Step 4 – Draw a Number LineStep 4 – Draw a Number Line

Locate the main Locate the main medianmedian 1212 using using a vertical line just above your a vertical line just above your number line:number line:

Step 5 – Draw the PartsStep 5 – Draw the Parts

Locate the Locate the lower medianlower median 8.58.5 and the and the upper medianupper median 1414 with with similar vertical lines:similar vertical lines:

Step 5 – Draw the Parts

Next, draw a box using the lower Next, draw a box using the lower and upper median lines as and upper median lines as endpoints:endpoints:

Step 5 – Draw the Parts

Finally, the Finally, the whiskerswhiskers extend out extend out to the data's smallest number to the data's smallest number 55 and largest number and largest number 2020::

Step 5 – Draw the PartsStep 5 – Draw the Parts

Step 6 - Label the Parts of a Box-and-Step 6 - Label the Parts of a Box-and-Whisker PlotWhisker Plot

1 23

54

Name the parts of a Box-and-Whisker Plot

Median Upper QuartileLower Quartile

Lower Extreme Upper Extreme

The interquartile range is The interquartile range is the difference between the the difference between the upper quartile and the upper quartile and the lower quartile. lower quartile.

Interquartile RangeInterquartile Range

14 – 8.5 =5.5

Lower Quartile = 5½

Q1

Upper Quartile = 9

Q3

Median = 8

Q2

4 5 6 7 8 9 10 11 12

4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12

Example 1: Draw a Box plot for the data below

Drawing a Box Plot.

Upper Quartile = 10

Q3

Lower Quartile = 4

Q1

Median = 8

Q2

3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15,

Example 2: Draw a Box plot for the data below

Drawing a Box Plot.

3 4 5 6 7 8 9 10 11 12 13 14 15

Upper Quartile = 180

Qu

Lower Quartile = 158

QL

Median = 171

Q2

Question: Stuart recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data.

Drawing a Box Plot.

137, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186

130 140 150 160 170 180 190cm

2. The boys are taller on average.

Question: Alia recorded the heights in cm of girls in the same class and constructed a box plot from the data. The box plots for both boys and girls are shown below. Use the box plots to choose some correct statements comparing heights of boys and girls in the class. Justify your answers.

Drawing a Box Plot.

130 140 150 160 170 180 190

Boys

Girls

cm

1. The girls are taller on average.

3. The girls show less variability in height.

4. The boys show less variability in height.

5. The smallest person is a girl.

6. The tallest person is a boy.