Measuring the Average: An Introduction to Measures of Central Tendency, Slides of Statistics

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Measures of Central

Tendency

TABLE OF CONTENTS

• Measures of Central Tendency
  • What are MEASURES OF CENTRAL TENDENCY?..................................................
• Measures of Central Tendency
  • Measures of Central Tendency
• Mode
  • Mode
• Median
  • Median
• Mean
  • Mean
• Glossary
• References...........................................................................................................................

● A distribution with 3 or more modes is called multi-modal.

● The mode is most useful when used with categorical (nominal, or ordinal) variables and when there is a relatively small sample size. The mode can be used with categorical variables because it does not require the data to be in a meaningful order.

● With large samples, it becomes very tedious to determine the mode.

Median

Median

● The median can only be used for ordinal, interval and ratio data. The median cannot be used for nominal data because the categories don’t have a meaningful order.

● To find the median, arrange all the scores in order and choose the middle score.

If there is an even number of scores in the distribution, the median is determined by taking the mean of the two middle scores.

In the case of ordinal data, if there is an even number of scores the mean cannot be calculated. In this situation, the lower of the two values is chosen as the median.

Mean

Mean

● The mean is determined by dividing the sum of scores by the total number of scores:

● The mean can only be used for interval and ratio variable data because the calculation of the mean requires that there is an equal interval between all the scores.

● The mean is generally the most useful measure of central tendency for interval and ratio data.

There is an exception: When there are outliers that skew the shape of the distribution, the mean will be pulled away from the majority of the scores, and towards an extreme end of the distribution.

In this situation, the mean is not an accurate descriptor of the centre of the distribution, and the median is a more appropriate measure.

References

Cohen, R. J., & Swerdlik, M. E. (2005). Psychological testing and

assessment: An introduction to tests and measurements. (6th^ ed.) NY:

McGraw-Hill.

Hamilton, L. C. (1996). Data analysis for social scientists. Scarborough:

Duxbury Press.

Utts, J. (2005). Seeing through the statistics. (3rd ed.). Toronto: Thomson

Brooks/Cole.

Wilson, J. H. (2005). Essential Statistics. New Jersey: Pearson Prentice Hall.