January 31, 2010
Measures of Central Tendency
Measures of Central Tendency (MCT) are used to
describe the general characteristics of a data set.
Mean: Sum of the data values divided by the total
number of data values (AKA the average)
Median: Middle number when the data values are
written in order and there is an odd number of data
values. For an even number of values, the median is
the average of the two middle numbers.
Mode: Data item that occurs most often; there can be
one mode, more than one, or no mode. To have no
mode, all data items appear the same number of times.
January 31, 2010
Ex: Eight local middle schools are raising money for Haiti. They
have raised $210, $310, $350, $310, $250, $780, $310, and $250
respectively. Calculate the mean, median, and mode for this data set.
Range: The range of the data set is the difference
between the smallest and largest values.
What is the range
for this data set?
January 31, 2010
Outlier: A data value that is much greater or less than the other data values.
An outlier can affect the mean of a group of data.
Is there an outlier
in this data set?
Identifying the Best Measure
One measure of central tendency may be better
than another to describe data. Choosing the best
measure will depend on what the data values are,
how many, and how large or small they are.
Next, we will see examples of data sets, which is the
BMCT to describe them, and WHY....
January 31, 2010
Favorite Movies of 7th graders: MODE; since the
data is non-numerical, the mode is the appropriate
measure. When determining the most frequently
chosen item, or when the data is non-numerical,
use the MODE.
Daily High Temperatures during a week in July:
MEAN; the likelihood of an outlier is low. When
there are no outliers, use the MEAN.
Distances Students in your Class travel to school:
MEDIAN; since one student may live much closer
or farther than anyone else, that student would be
an outlier. When an outlier may significantly
influence the mean, use the MEDIAN.