Measures of Central Tendency
Instructional objectives for the lesson
1. The student will be able to define what a mean of sample is.
2. The student will be able to define what the median of sample is
3. The student will be able to define what the mode is.
4. The student will be able to calculate the mean of a sample.
5. The student will be able to calculate the median of a sample.
6. The student will be able to identify the mode of a sample.
Central Tendency
A measure of central tendency is a measure used in statistics that attempts to describe a set of data with a one value that represents the middle or typical of its distribution.
There are three main measures of central tendency: the mode, the median and the mean. Depending on what you are trying to describe and the type of data you are using, you would use each of these for different things. Below will be a discussion of these measures and when you would use them.
Mode
The mode is the value in a distribution that occurs the most commonly.
Look at the values in this data set below:
54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60
The most commonly occurring value is 54, therefore the mode of this distribution is 54.
If these values were ages of retirements for a group of people, this might be useful. That is to say that this may answer the question, “when do most people in this group retire?
However in this grouping, because the mode is at the lower end of distribution, this would not tell you what are the true centers or average age of this group. To answer these questions, the median or mean may be more appropriate.
Median
The median is the value in the distribution that appears physically in the middle when the values are arranged in ascending or descending order. That is to say, the median is the point where half of the values are above and half the values are below.
So, if we have and odd number of values such as 11, the value of the 6th value in ascending or descending order would be the median. See below for further explanation.
If we look at the same data set we used above when the mode was explained, the mode would be 57 because it is the sixth value in the group.
54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60
However, if we had an even number of values for a distribution, say 10, the median would actually be an average of the 5th and 6th value. The median below would be 55.5 because it is the average of the 5th and 6th values in the distribution.
52, 54, 54, 54, 55, 56, 57, 57, 58, 58,
The median is especially useful when there outliers or a distribution is skewed where a mean is more vulnerable to these. Median is often used to describe income of a sample because of the tendency for outliers. The median is not useful when describing nominal, or categorical data, such as gender or race.
Mean
The mean is the arithmetic average. It is calculated by adding up all the values in a distribution and dividing it by the number of values in that distribution.
If we look at our same data set again, the mean would be 56.6.
54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60
Adding all the values (54+54+54+55+56+57+57+58+58+60+60) equals 623. Then if you divide it by the number of values in the distribution (11), your average (mean) which equals 56.6.
If you are looking for the average of a set of values, which is quite common, the mean is the measure of central tendency used. Similar to the median, the mean tells you nothing if you try to use it in categorical data. Unlike the median, the mean can be influenced heavily by outliers and skewed data.
Instructional Video
Below is a link to an instructional video on measures of central tendency in two parts
Part 1 - http://youtu.be/1Hftk0lOdWE
Part 2 -http://youtu.be/Iov6B-hp4Sw
Additional Links
Below are some links that will give you additional information on central tendency
http://www.socialresearchmethods.net/kb/statdesc.php
http://onlinestatbook.com/2/summarizing_distributions/measures.html
http://www.psychstat.missouristate.edu/introbook/sbk13.htm
Discussion Question
You and your classmates will be sent an email for access to a Googledoc to discuss this question.
Remember your responses should be respectful of other classmates feedback in this discussion.
If you are using the variable age in research, present some scenarios when it would be appropriate to discuss age using the mode, when it would be appropriate to use the median and when it would be appropriate to use the mean? Be specific and detailed. Please respond to two of your classmates ideas on the Google Doc.
Assignment
By completing and submitting this assignment you are certifying it is your work. Please refer to the student's code of conduct as it discusses the ethics and responsibilities of earning an education at Youngstown State University.
Copy and paste the assignments into a Word document and complete the assignments.
Please submit your assignmnents to Nick Cascarelli at nvcascarelli@ysu.edu.
Matching. Place the letter for the description of each central tendency measure to the one that you feel best matches.
1. Mode _______ a. The arithmetic average
2. Median _______ b. The middle value
3. Mean _____ c. The most common value
Calculating the central tendency measures.
Using the data set below calculate the mode, median and mean.
5, 6, 6, 8, 9, 12, 13
Mode ______
Median ____
Mean_____