step 1 – order numbers order the set of numbers from least to greatest
TRANSCRIPT
Step 1 – Order Numbers
Order the set of numbers from least to greatest.
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
Find the lower, or first quartile and upper, or third quartiles. These are considered the lower and upper medians. These are the middle numbers on each side
of the median. What are they in this example?
Step 3 – First & Third Quartiles
Interquartile Range
The interquartile range is the difference between the upper quartile and the lower quartile.
14 – 8.5 =5.5
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 median using a vertical line just above your number line:
Step 5 – Draw the Parts
Locate the first quartile and the third quartile 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
Outliers are not included in the box and whisker plot. They are shown as an asterisks on the number line. For example, if the data set had an outlier of 24, it would
be show as seen below.
Step 6 - Label the Parts of a Box-and-Whisker Plot
1 23
54
Outliers are not included in the box and whisker plot. They are shown as an asterisks on the number line.
Median Third QuartileFirst Quartile
Lower extreme Upper extreme2
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.
115, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186
130
140
150
160
170
180
190
cm
Practice
Use the following set of data to create a box plot.
3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220
Median
What is the median or 2nd quartile?
3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220
The median is 39
1st Quartile
What is the 1st quartile?
3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220
The lower quartile is 11
3rd Quartile
What is the 3rd quartile?
3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220
The third quartile is 61
What is the Interquartile Range?
50
Outliers
An outlier is a number that falls outside the limits.
Are there any outliers?
The outlier is 220
Upper Extreme
What is the upper extreme?
3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220
The upper extreme is 99
c
Lower Extreme
What is the lower extreme limit?
3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220
The lower extreme is 3
Graphing The Data
Now use the data you have collected to create a box and whisker plot.
Independent Practice – Create box plots for the following data
12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10
Example 1: Draw a box plot for the data below.
6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10
Example 2: Draw a box plot for the data below.
Worksheet 1