{ Box-and-Whisker Plots

Median, Quartiles, Inter-Quartile Range and Box Plots. Measures of Spread The 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 greatest Step 1 – Order Numbers

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

3. Find the lower and upper medians or quartiles. These are the middle numbers on each side of the median. What are they? Step 3 – Upper & Lower Quartiles

Now you are ready to construct the actual box & whisker graph. First you will need to draw an ordinary number line that extends far enough in both directions to include all the numbers in your data: Step 4 – Draw a Number Line

Locate the main median 12 using a vertical line just above your number line: Step 5 – Draw the Parts

Locate the lower median 8.5 and the upper median 14 with similar vertical lines: Step 5 – Draw the Parts

 Next, draw a box using the lower and upper median lines as endpoints: Step 5 – Draw the Parts

Finally, the whiskers extend out to the data's smallest number 5 and largest number 20: Step 5 – Draw the Parts

Step 6 - Label the Parts of a Box-and- Whisker Plot Name the parts of a Box-and-Whisker Plot MedianUpper Quartile Lower Quartile Lower ExtremeUpper Extreme

The interquartile range is the difference between the upper quartile and the lower quartile. Interquartile Range 14 – 8.5 =5.5

Lower Quartile = 5½ Q1Q1 Upper Quartile = 9 Q3Q3 Median = 8 Q2Q , 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 Q3Q3 Lower Quartile = 4 Q1Q1 Median = 8 Q2Q2 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

Upper Quartile = 180 QuQu Lower Quartile = 158 QLQL Median = 171 Q2Q2 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, cm

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 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.