MOD 9 QUANTIFYING VARIABILITY RELATIVE TO THE MEDIAN
(This is a modified version of a Los Medanos College activity developed for their Path2Stats program.)
Learning Objectives
• Create and interpret different graphs of the distribution of quantitative data.
• Summarize and describe the distribution of quantitative data in context. Describe the overall
pattern (shape, center, and spread) and striking deviations from the pattern.
• Compare distributions from two or more groups.
Variability, Quartiles, and the Interquartile Range
A statistician will describe a distribution by describing the shape, giving a measure of central tendency
(mean or median), and also giving a measure of variability (a.k.a. spread).
1)
Find the median for this set of data.
Statisticians measure spread relative to the median by marking the quartiles. Quartiles divide the
data into four groups, with 25% of the data in each group. The median is the second quartile.
WAIT!!! Let's work through this one together as a class.
Create a boxplot for these data. Mark the quartiles on the number line. Use the quartile marks to
make a box. Then mark the lowest data value and the highest data value. Connect these to the box
with a horizontal line.
2)
When we have a distribution, we can set dividers with “equal widths” or “equal counts”.
a) For the first graph, are the four areas
created with “equal widths” or “equal
counts” dividers?
Which kind of dividers are used in the
second graph (equal widths or equal
counts)?
b) Write percentages representing the percent of data in each of the four shaded sections for
both graphs.
c) Which kind of divider is related to a boxplot?
Draw the boxplot for this data. Show the percentages above your boxplot.
d) Which kind of divider is related to a histogram?
Draw a histogram for this data (bin width = 4). Show the percentages above your histogram.
3)
Match the histograms to the boxplots.
4)
Make up a data set (n=11) that fits this pair of graphs. Then find a different data set (n = 11) that
also fits these two graphs.
5)
Make up a data set (n=10) with the most amount of spread possible that fits this boxplot. Then
make up a data set (n=10) with the least amount of spread possible that fits this boxplot.
6)
Make up a data set with 10 numbers that matches this boxplot. Make a histogram of your data.
7)
Draw a boxplot for the data shown in the dotplot.
8) WAIT! We’ll work through this one together as a class. Use the 1.5 IQR criterion to find the
outliers (if any) for the following data set.
9) Use the 1.5 IQR criterion to find the outliers (if any) for the following data set.
Tallest Buildings
Options
55.5
30
40
Circle Icon
50
Box Plot of Stories
72
60
70
Stories
80
90
100
110