In the analysis of individual observations, or ungrouped data, consideration will be given to all levels of measurement to determine which descriptive measures can be used, and under what conditions each is appropriate.
One of the most widely used descriptive measures is the ‘average’. One speaks of the ‘average age’, average response time’, or ‘average score’ often without being very specific as to precisely what this means. The use of the average is an attempt to find a single figure to describe or represent a set of data. Since there are several kinds of 'average', or measures of central tendency, used in statistics, the use of precise terminology is important: each ‘average’ must be clearly defined and labelled to avoid confusion and ambiguity. At least three kinds of common uses of the ‘average’ can be described:
1. An average provides a summary of the data. It represents an attempt to find one figure that tells more about the characteristics of the distribution of data than any other. For example, in a survey of several hundred undergraduates the average intelligence quotient was 105: this one figure summarizes the characteristic of intelligence.
2. The average provides a common denominator for comparing sets of data. For example, the average score on the Job Descriptive Index for British managers was found to be 144, this score provides a quick and easy comparison of levels of felt job satisfaction with other occupational groups.
3. The average can provide a measure of typical size. For example, the scores derived for a range of dimensions of personality can be compared to the norms for the group the sample was taken from; thus, one can determine the extent to which the score for each dimension is above, or below, that to be expected.
One of the most widely used descriptive measures is the ‘average’. One speaks of the ‘average age’, average response time’, or ‘average score’ often without being very specific as to precisely what this means. The use of the average is an attempt to find a single figure to describe or represent a set of data. Since there are several kinds of 'average', or measures of central tendency, used in statistics, the use of precise terminology is important: each ‘average’ must be clearly defined and labelled to avoid confusion and ambiguity. At least three kinds of common uses of the ‘average’ can be described:
1. An average provides a summary of the data. It represents an attempt to find one figure that tells more about the characteristics of the distribution of data than any other. For example, in a survey of several hundred undergraduates the average intelligence quotient was 105: this one figure summarizes the characteristic of intelligence.
2. The average provides a common denominator for comparing sets of data. For example, the average score on the Job Descriptive Index for British managers was found to be 144, this score provides a quick and easy comparison of levels of felt job satisfaction with other occupational groups.
3. The average can provide a measure of typical size. For example, the scores derived for a range of dimensions of personality can be compared to the norms for the group the sample was taken from; thus, one can determine the extent to which the score for each dimension is above, or below, that to be expected.
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