Page 275 - ABCTE Study Guide_Neat

The range is another measure that gives information about a set of data, but it is not a measure of central
tendency. That’s because it doesn’t define the center of the distribution of the data. It’s actually called a
measure of dispersion, because it describes the way that the data are dispersed.

Measures of Central Tendency

The Mean

The mean of a set of data is the arithmetic average. That’s the one you’re used to computing. It’s not
called the average in statistics, because there are different kinds of averages.

To find the mean, simply add up the values in a set of data and divide by the number of values in the
set.

The Median

The median of a set of data is the value in the middle of the set. To find the median, order the values in
the set from least to greatest (or from greatest to least).

The Mode

The mode of a set of data is the value that occurs most often. The mode of the set {4, 5, 3, 5, 4, 2, 1, 2, 4}
is four, because four occurs more often than any other number in the set.

Unfortunately, it’s not as simple as it sounds. Sometimes a set may have more than one mode or no
mode at all.

So how many modes are in the set {5, 4, 2, 4, 5, 2}? The answer is three. Every value in the set is also a
mode of the set. Take some time to convince yourself that this is true.

A Measure of Dispersion: The Range

The range of a set of data is the difference between the greatest and least values in the set. That makes
the range positive. To find the range of a set of data, subtract the least value in the set from the greatest
value.

You can see that the range gives a pretty poor summary of a set of data, because it relies on only two
values in the set. What measure would be more meaningful for a set of salaries that included yours and
Bill Gates’s?

Typically, the median of a set like this one is most meaningful, because the range of values is so great.

Question

For the set below, which measure is least?

{1, 8, 7, 3, 7, 6, 5, 6, 2}

A Mean