¶ … Scores

Generally speaking, a set of test scores such as those provided would not be considered continuous data, as in most test scenarios there are a finite number of scores possible. If a test has 100 questions and is worth one point per question, then the only possible scores are those whole numbers from 0 to 100 -- a finite set of responses rather than an infinitely reducible continuum. In order for this data set to be considered continuous, it would need to be demonstrated that partial points were possible to a degree that enabled a full continuum of scores to be presented.

As the data set represents test scores, it must certainly be considered at least an interval scale, with the two point difference between 79 and 81 the same interval as the two points between 97 and 99. It can also be inferred that these are percentages, and that a score of 0% would be possible, and the existence of this zero would give each score on the scale an absolute position to be related to, making this a ratio scale. As this is a higher order of measurement, more meaningful analysis can be made regarding the distribution of the data. An examination of the accompanying chart and graph make certain basic elements of this data set clear.

For such a small data set, there is a fair amount of central tendency, with the mean, median, and mode all relatively tightly clustered from 80 to 84.5. Variance is somewhat large, with a standard deviation of more than 6 in a range of only 22, but again with such a small data set and limited range this is not too unexpected. There is a slight skew to the left when only the range of achieved scores is examined, though if the chart were expanded to include the full range of possible scores (0 to 100) there would be a very strong skew to the right. Kurtosis is not too extreme, and is cut by the spike at the top end of the scores.

Test Score Analysis

SCORES:

SUM. STATS:

76

77

Mean:

84.5

79

Median:

82.5

79

Mode:

80

79

80

Range:

22

81

Std. Dev: