Box Plots
In this exploration you will investigate properties of
box
plots, reinforcing the concepts in Lesson 2.1 of Discovering
Advanced Algebra: An Investigative
Approach.
Sketch
A five-number summary is
a good way to describe a data set. The five points used are the maximum
and minimum data points, the median (which divides the data set in
half), the first quartile (the median of
the first half), and the third quartile (the median
of the second half). These numbers are displayed visually with a box
plot, also called a box-and-whisker plot.
This sketch allows you to see the box plot
for 19 data points whose values can range from 0 to 30. When you drag
any of the data points, the box plot will be updated dynamically.
Investigate
- About how many data points lie along each of the
whiskers? Explain.
- What percentage of the data values are represented by
the left whisker? The right whisker?
- What happens to the box plot when all of the data
points are close together? When they are far apart?
- How can you make long whiskers? Short whiskers?
- How can you make a symmetric box plot?
- How can you make the box plot skewed to the left?
Skewed to the right?
- Can different data sets have similar box plots?
- The difference between the third quartile and the
first quartile is the interquartile range or IQR.
It is the same as the length of the box in the box plot. What fraction
of the data points fall between the first and third quartiles of a box
plot? Explain.
- How can you move points to make the interquartile
range larger?
Smaller?
- How is the median related to the first quartile and
the third quartile? Test your answer by dragging data points.
- Outliers are data values that differ
significantly from most of the data. How are the outliers of a data set
related to the whiskers of the box plot?
- Do you think the box plot gives a good picture of a
large number of data points? Explain.
|
