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2.3 Descriptive Statistics – Center and Position
Histograms provide us with a great visualization of the overall distribution of values. A
distribution describes the layout of the values of a quantitative or categorical variable. To further
describe the differences between two similar distributions, it is helpful to use statistics that
describe center, location, and spread.
2.3.1 Mean and Median
To make peace with some regularly occurring notation in statistics, we will use
mean “the sum of.” For instance,
(“sigma”) to
Let‟s say that we have a set of variable values. To distinguish each of these “ ‟s” we‟ll use
subscripts, denoting them:
Then, to indicate that we want to sum these values across all subscripts, we would write:
Which means, “sum up all
values in the dataset,” or
Using this new notation, we already know how to calculate the mean:
Mean – x-bar notation
The mean value, or average, of a dataset containing
values can be written as:
̅, is used to denote the mean of a sample and can be read as “x-bar.”
A common point of confusion for students is the difference in the subscript and the
denominator . Many people think that the subscript should be to match the number of
elements in the dataset. However, specifically refers to the very last value in the dataset. We
treat the as an index that goes across all subscripts from 1 all the way up to and including . To
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