MEASURES OF CENTRAL TENDENCY

MODE

·        The most frequent score in a distribution

·        The actual values of the scores are not considered when calculating the mode

·        Used with nominal scale data

·        Used when only a very simple description of scores is needed

·        Has limited application and value

 Table 3.4  (p. 88)
Favorite restaurants named by a sample of n = 100 students. Caution: The mode
 is a score or category, not a frequency. For this example, the mode is Luigi’s, not
 f = 42.

MEDIAN

·        The middle score in a distribution (central score in an ordered distribution)

·        Can be used with ordinal scale data

·        Used when there are very extreme scores (outliers) or the distribution is not normal

·        More information taken into account than with the mode

·        Used primarily when the mean cannot be used

Figure 3-5  (p. 82)
The median divides the area in the graph exactly in half.

 Figure 3-7  (p. 84)
A distribution with several scores clustered at the median. The median for this distribution is positioned so that each of the five boxes above X = 4 is divided into two sections, with 1/5 of each box below the median (to the left and 4/5 of each box above the median (to the right).

MEAN

·        Statistical average of scores (total divided by the number of scores)

·        Value dependent on each score in a distribution

·        Used with interval or ratio scale data

·        Can be misleading if there are very extreme scores or the distribution of scores is not normal

·        Most widely used and informative measure of center

CHARACTERISTICS OF THE MEAN

·        Every value in a set of scores contributes equally in the calculations.

·        The mean can be considered as a point of balance in the distribution ("center of gravity"). The sum of all the deviations from the mean is zero.

·        The mean is the point about which the sum of the squared deviations is minimized (compared to the case where any other number would have been used)