A Box and Whisker What???
A detailed guide to making and interpreting Box and Whisker Plots.
Mrs. C. Fisher – Whetstone Elementary
Box and Whisker Plots
Box and Whisker Plots are a method used to analyze a given set of data.
Let’s use some pretend math scores as a sample data set:
77,81, 83, 85, 85, 86, 86, 87, 89, 90, 93, 93, 97, 100
Step 1: Find the Median
We must first identify the median of the data set. Remember that the median
is the middle number when the data set is ordered from least to greatest. If
there is an even number of numbers in the data set, then we must find the
mean of the two middle numbers.
There are 14 numbers so there is no true middle number!
77,81, 83, 85, 85, 86, 86, 87, 89, 90, 93, 93, 97, 100
86 and 87 are the two middle numbers. What is their mean.
86 + 87 = 173
173 divided by 2 is 86.5…..The Median
Not those whiskers, silly!!
Lower Extreme
Upper Extreme
77,81, 83, 85, 85, 86, 86, 87, 89, 90, 93, 93, 97, 100
Step 1: Find the Median
Step 2: Find the Upper and Lower Extreme
This step is easy. The Upper and Lower Extremes are simply the
smallest and largest numbers in the data set. In our example: 77 and
100
Lower
Quartile:
85
Median
86.5
Upper
Quartile
93
77,81, 83, 85, 85, 86, 86, 87, 89, 90, 93, 93, 97, 100
Lower Extreme
Upper Extreme
Step 1: Find the Median
Step 2: Find the Upper and Lower Extreme
Step 3: Find the Upper and Lower Quartile
The Upper Quartile is simply the median of the upper half of the data
set. The Lower Quartile is the median of the lower half of the data
set.
Put It All Together
Lower Extreme: 77
Lower Quartile: 85
Median: 86.5
Upper Quartile: 93
Upper Extreme: 100
Create a number line that spans the set of data: for our example 70-100
Place a vertical line above the Quartiles and Median.
Place a point above the Extremes.
Connect the vertical lines with horizontal lines to make a rectangle/box.
Draw a line from the box to the Extremes
٠۰
70
75
٠۰
80
85
90
95
100
You’re Done!!
Analysis:
When analyzing Box and Whisker Plots, it is common to
discussing Quartiles (fourths) or percents.
•50 % of students did better than 86.5
•The top 25% of students scored about 93 or higher
70
75
80
85
90
95
100