Algebra 1 Notes SOL A.10 Measures of Central Tendency Mr. Hannam Page 1

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.

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 1

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 peopleinvolved 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) / ______/ maximum value (upper extreme) / ______
lower quartile / ______/ upper quartile / ______

c) Create a box-and-whisker plot of the data.

  • 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?