OMS Technology Staff will add in more recent samples of produced reports.

Individual Report (PDF)
Descriptive Report: Part One (PDF)
Descriptive Report: Total (PDF)

The distribution of scores is the first level of score summarization. The distribution is presented in several ways:

The FREQUENCY is the number of students with each score.

The CUMULATIVE FREQUENCY is the number of students at or below each score.

The PERCENT is the percent of students that have each score.

The CUMULATIVE PERCENT is the percent of students at or below each score.

The PERCENTILE RANK and STANDARD SCORE corresponding to each raw score also are shown.

Statistics provide a second level of summarization of the score distribution. Two characteristics of the distribution that are of primary interest are central tendency and variability. Central tendency refers to the score that is most representative of the entire distribution. Variability refers to the tendency of the scores to be either spread out or bunched up around the center.

Three measures of central tendency are provided.

1. The MEAN is the arithmetic average, the sum of all scores divided by the total number of scores. The mean is the statistic that most people think of as "the average." It is ordinarily the best measure of central tendency if the units on the score scale are equal, which is a reasonable assumption for most tests especially if the distribution of scores is symmetrical. Extreme scores heavily influence the mean. Consequently, if the distribution is skewed, i.e., there are extreme scores at one end that are not balanced by extreme scores at the other; the mean may not adequately represent the center of the distribution.

2. The MEDIAN (50TH PERCENTILE) is the point on the score scale where half the cases lay either above or below. Because extreme scores do not influence the median, it represents the central tendency of skewed distributions better than the mean.

3. The MODE is the most frequently appearing score. It may be thought of as the most typical score. However, the same frequency may occur at more than one score, so there can be more than one mode. The mode is indicated on the score distribution.

VARIANCE AND STANDARD DEVIATION. The variance is the average squared deviation around the mean. The mean is subtracted from each score; the resulting difference is squared; and the sum of the squared differences is divided by the total number of scores. The standard deviation is the square root of the variance, and it represents a distance on the score scale. If the test scores are distributed as a normal curve, 68 percent of the scores are between one standard deviation below the mean and one standard deviation above the mean while 98 percent of the scores are between plus and minus two standard deviations.

The RANGE is the distance on the score scale that includes all the scores, calculated by adding 1 to the difference between the highest and lowest scores. Because the range depends on the values of just two scores, it is not a reliable, stable statistic.

The distribution statistics report provides other statistics from which other measures of variability can be obtained: the 10TH, 25TH, 75TH, and 90TH PERCENTILES, which are the points on the score scale that divide the distribution of scores into the specified percentages. The inter quartile range is the distance between the 25th and 75th percentiles. By definition, 50 percent of the scores are included in the inter quartile range. The semi-inter quartile range, which is half the inter-quartile range, is often used with the median, just as the standard deviation is used with the mean in order to describe the variability and central tendency of a distribution.

Other items on the report include the total number of scores (Group Size), the sum of scores and the sum of squared scores (which may be used in additional statistical calculations), the highest and lowest obtained scores, the highest possible score and the percentages that the mean is of the highest possible score and the highest obtained score. The last two measures indicate the difficulty of the test. If the percentages are high (e.g., 80 or above), the test was easy for this group. If the percentages are low (e.g., below 50), the test was hard for this group. (The highest possible score and the percent that the mean is of the highest possible score are not printed on part-score reports because they cannot always be determined.)

The Histogram Report, which is optional, appears as the second page of the distribution statistics. This report shows, for each raw score, a row of asterisks. Each asterisk represents one student, thus graphically portraying the distribution of scores. Examination of the histogram can give a quick indication of whether or not the scores approximate a normal distribution, are skewed or exhibit other abnormalities. If the number of different scores is such that the histogram exceeds one page, there is an optional report that is able to sufficiently downsize the scores in order to keep them at the one page length.