Algebra 1 Notes SOL A.10 Measures of Central Tendency
Mr. Hannam
Name: _______________________________ Date: _____________ Block: _______
Measures of Central Tendency
In data analysis, we use measures of central tendency (also called averages). We use them
to measure a middle value for a set of values (called a dataset) that best describes the data
in the dataset.
Mean
Median
Called x (x bar). We sum a dataset and divide by its sample size (the
x  x2  ...xn
number of data points in the data set). Formula: x  1
n
Middle number of a dataset written in numerical order. If there is an even
number of data points, then we take the mean (see above) of the middle
two numbers.
Mode
The value that occurs most frequently in a dataset.
Range
The difference of the greatest and least values in a dataset (not really a
measure of central tendency, but a measure of the spread of data).
The mean is most often used, but sometimes it may not give the best measure of central
tendency. For example, the dataset below shows home prices in a location. Find the mean,
median, and mode of the data, and assess which measure best describes the data.
{$625,000, $585,000, $590,000, $350,000, $615,000, $570,000, $615,000}
Mean
Median
Mode
Which measure gives us the best representation of housing prices? Why?
Comparing Measures of Central Tendency
The chart at right shows the difference in grades for two students in
a math class.

What is the difference of the means (rounded to the nearest
whole number) of the two students?

Which student has the highest median grade?

Which student has the lowest mode?
Algebra 1 Notes SOL A.10 Measures of Central Tendency
Mr. Hannam Page 2
Box-and-Whisker Plots
There are various ways to graphically represent data: scatter plots, stem-and-leaf, and
histograms are some examples. We will look at box-and-whisker plots.
An example of a box-and-whisker plot is shown
at right with its parts labeled:
median - midpoint of data
lower quartile - midpoint of lower half of data
upper quartile - midpoint of upper half of data
lower extreme - smallest data value
upper extreme - largest data value
interquartile range – difference between upper and lower quartiles.
Example: A researcher collected ages of people involved in a study. The data is shown
below:
{18, 26, 21, 39, 27, 16, 30, 47, 31, 35, 52, 18, 45, 67, 51, 59, 63}
Construct a box-and-whiskers plot that represents the data.
a) Put the data in order from least to greatest
b) Find the following data:
median
minimum value
(lower extreme)
lower quartile
_____________
_____________
_____________
maximum value
(upper extreme)
upper quartile
_____________
_____________
c) Create a box-and-whisker plot of the data.
** Be careful finding quartiles. **
If you have an odd number of data points, DO NOT including the median when finding
quartiles.
If you have an even number of data points, INCLUDE the median when finding quartiles.

Each quartile represents percentages, with 25% of the data between each quartile.

In the above box-and-whisker plot…
 What percentage of data is greater than 35?

What percentage of data is greater than 23.5?

What percentage of data is less than 51.5?

What value is 25% of the data less than?