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7.1
Central Tendency
P
urpose
The role this topic plays in quantitative reasoning
One of the goals of descriptive statistics is to describe the characteristics of a large set of data with a few
numbers. Perhaps the most relevant number is a measure of central tendency. It is a number that describes
where the data cluster around a central area. Measures of central tendency provide useful information
such as, “How much can I expect to earn at that company?” or “Can I afford to purchase a house in that
neighborhood?” There are various measures of central tendency that can be defined to represent a data
set. It is critical to determine in each situation which measure — the mean, median or mode — is the
best measure of central tendency. Understanding the concepts together with the computational methods
will enable you to describe the behavior of a data set and make predictions about future data elements
drawn from the same population.
L
earning Goals
What you should learn while completing this activity
1. Become proficient in computing each major measure of central tendency.
2. Determine which measure of central tendency is most appropriate for a given data set.
3. Present central tendency visually
4. Predict the relationship among the mean, median and modes from different data sets
D
iscovery
Finding out for yourself
Which single number would best describe the heights of adult males in the USA? Which single number
would best describe the heights of adult females in the USA? How different would those two numbers
be? Would you expect the means and medians to be similar? Would you expect that the central tendency
numbers would be the same for various ethnic groups?
If you wanted to purchase a home in a certain community what measure of central tendency would you
use to determine if you could afford such a purchase? Would you expect the means and medians to be
different?
W
hat Do You Already Know?
Tapping into your existing knowledge
1. What are five types of averages that you know?
2. Is the average a mean or median?
3. Do you know how to calculate the mean of a series of numbers?
4. Do you know how to calculate the median of a series of numbers?
5. Have you heard of a
mode
? What is it?