Measures of Central Tendency

Central Tendency “Values that describe the middle, or central, characteristics of a set of data” Terms used to describe the center of a group of scores –Most common score –Typical score –Average score

The Mode Score that occurs most frequently No formula to calculate –Foun by inspection Simple frequency distribution vs. grouped frequency distribution

Mode: Advantage and Disadvantages Advantages –Easy to determine –Quick estimate of the center of the group –In a normal distribution it is a good description of the central tendency –Can be used on an ordinal scale Disadvantages –It is unstable –It is a terminal statistic –Completely disregards extreme scores

The Median Score associated with the 50th percentile Middle score –Divides data set in half

The Mean Statistical name for the average Most commonly used measure of central tendency Gives weight to each score according to relative distance from other scores in data set –Very sensitive –Slight change in any score will change the mean

The Mean Advantages –Considers all information about the data –Provides basis for many other calculations Disadvantages –See above –Outliers can skew average to the extreme score Precision of mean should not exceed precision of data set

Calculating Mean Rank order distribution Simple frequency distribution

Relationship Among the Mode, Median, and Mean With a normal distribution –All three measures fall at or near the same value When data are skewed measures are no longer identical

Which Measure to Use? Mode only if a rough estimate of central tendency is needed –Only when data are normally distributed Median if: –The data are on an ordinal scale –Middle score of group is needed –Most typical score is needed –Curve is badly skewed by extreme scores

Which Measure to Use? Mean if: –Curve is near normal, data are of interval or ratio type –All available information from the data is to be considered –Further calculations are to be made Standard deviations Standard scores