Getting Ready for AP STATISTICS: MEAN-MEDIAN-MODE

MEAN - MEDIAN - MODE

For those of us preparing to earn a 5 on the AP Statistics exam next spring, calculating mean - median - mode should be as natural as eating ice cream on a hot summer’s day.  The measures of central tendency were introduced in upper elementary math classes, but it isn’t until now that the various uses have important implications.  

CALCULATING MEASURES OF CENTRAL TENDENCY

MEAN is the same as “average”  or “arithmetic mean.”
     Add all of the elements and divide the sum by the number of elements.

MEDIAN is the middlemost.  Think of the middle of the street...that’s the median. 
One very easy way to find the median in a small group is to first put all numbers in ascending order. Then count from the right and left simultaneously until you get to the middle.

If there are an odd number of elements, there will be one in the middle that can’t be matched from both the right and left......the median.

If there are an even number of elements, the median is the AVERAGE of the two in the middle.

MODE is the most frequently appearing element.

USING CENTRAL TENDENCY TO DESCRIBE DATA

In Statistics, these measures are used to describe the “typical” element and the relative usefulness of each is determined by the level of measurement.  (Watch this site for an upcoming blog, "Getting Ready for AP Statistics: Levels of Measurement" and share examples with other followers.)

NOMINAL (entries are categories or qualitative data)......MODE

ORDINAL (qualitative or quantitative data)....................MEDIAN

INTERVAL (quantitative data)
--- Symmetric.............................................................MEAN
--- Skewed.................................................................MEDIAN


RATIO (quantitative data)
--- Symmetric.............................................................MEAN
--- Skewed.................................................................MEDIAN

A MEAN is useful only for interval or ratio data.  It considers all of the elements in the sample and is influenced by outliers.  The mean is pulled toward an extreme.

A MEDIAN is useful for all quantitative data: ordinal, interval, and ratio levels and is not effected by an extreme outlier.

A MODE is the only useful descriptor for nominal measurements.  It can be applied in all levels of measurement but may not exist or be meaningful in all cases.

 MEAN - MEDIAN - MODE ON A FREQUENCY GRAPH

  

 

USING A CALCULATOR FOR RECORDING MEAN - MEDIAN 

If you're using a TI-84 or similar grapher, check out the "LIST" and "STAT" buttons.  There are options for finding mean and median after listing the elements in a set.  While you're at it, find the owner's manual for the calculator you'll be using in class and look over the directions for inputting a list and calculating various statistical values.

Keep watching this site for more "Previews" of AP Stats, AP Calc, and other classroom courses.  Let's be prepared before school resumes!