Hi, I'm Dr. Todd Daniel and you're watching Statistics for the Flipped
Classroom. Last time, I showed you how to display data with pictures. Now, I'm going
to teach you how to display your data with numbers. There are some specific
numbers that we want to know about our data, and foremost we want to know where
is the center of the data. There are three ways that we can describe central
tendency: mean, median, and mode. I'm going to teach you when we will use each
measure of central tendency, and how to compute each one.
Let's get started.
We have two important questions about our data set. The first question is; what
single number best represents our data? Our second question is whether the
scores are packed together or spread out. The answer to our first question about
the most representative score is going to be some measure of central tendency.
A measure of central tendency indicates where the center or the middle of the
distribution tends to be. So you took a test, and you got 94%.
You may have done exceptionally well,
or maybe not. Perhaps you're really smart or perhaps the test was really easy.
If I just tell you the raw scores; 80, 94, 73, 88, 86, 72, then you still don't really
know that much, but if you know that you scored 94 and the class average was 80.5
then you know that you did really well.
A measure of central tendency answers the question of whether the scores are
generally high or generally low. For example, if I tell you about my friend
who is a basketball player,
what do you assume about his height? Based on what you know about basketball
players in general, you might assume that his height is above average because you
know that the height of basketball players is generally high. If I tell you
about my friend who is a horse jockey, you might assume that his height is
generally low. These estimates are based on what you already know about what the
heights of certain individuals tend to be. You are using a measure of central
tendency. Measures of central tendency offer the benefit of simplification.
The whole sample of raw data is difficult to understand. A measure of central tendency
gives us a single number that represents the entire data set. Central tendency
also has the benefit of prediction. Knowing a measure of central tendency
can help us to predict other scores
or estimate future needs and this is true even if the measure of central
tendency is not in the actual data set. If I tell you that the average family
has 2.3 children, but that our city is projected to grow by 1,000 families in
the next five years, how many new classroom seats will we need in public
schools? Although no family who moves to our town literally has 2.3 children, that
average is still very useful for predicting how many children will be
entering the school system. Determining which measure of central tendency to use
depends upon two things.
First, it depends upon the scale of measurement; nominal, ordinal, interval, or ratio.
For instance, the mean is typically used with interval or ratio level data. Second, our
choice of a measure of central tendency depends upon the shape of the
distribution. If the distribution is highly skewed or kurtotic, we may choose a
specific measure of central tendency. There are three measures of central
tendency that we will learn about; mean, median, and mode.