Descriptive Statistics: Definitions of Terms in Data Results Tables

Taken from R.E.A. Report – August 10, 2001

N represents the total number of students for whom data were received. Small n represents the number of students for whom data is available for the particular item represented in the table. Note that the values for n may not be the same across all tables. This discrepancy in groups of tables is a result of two factors: either no data were provided for that particular item, or the data that were submitted were erroneous (e.g., score was outside of the range of possible responses) and therefore not included in the analysis.

The minimum score on a test is the lowest score that any student achieved on that particular administration of the test. (It is not necessarily the minimum possible score on the test). The maximum score is the highest score that any student achieved on that particular administration of the test. By subtracting the minimum score from the maximum score to obtain the range, it is possible to assess the spread of scores between the highest and lowest performing students.

The mean represents the average of all the scores, which indicates the typical score for each assessment. The mean should be interpreted in relation to the maximum possible score in order to provide useful, comparative information.

The median represents the midpoint of the scores for all the students at that grade level; in other words, half the students scored above this value and half below the value.

The modal score (mode) for each assessment represents the most frequently occurring score. If two scores occur equally as often, the mode is the mean of the two most frequently occurring scores.

The standard deviation (or the average amount scores vary from the mean) provides information on the variability in responses. A large standard deviation in relation to the mean suggests that there were large disparities in students’ responses (i.e., some students did very well, while others did quite poorly). A small standard deviation indicates that most students scored fairly close to the mean.

In tables that include many percentages, type of percentage used is specified. A column percentage (col%) indicates that each percentage should be read as a proportion of the column total. A row percentage (row%) indicates that each percentage should be read as a proportion of the row total.

Please note that percentages in tables may not add up exactly to 100 percent. This is due to rounding error. For example, three categories might represent 50.2 percent, 25.4 percent, and 24.4 percent of the total, which adds up to 100.0. However, because percentages are rounding off to zero decimal places, you would see 50, 25, and 24, which only add up to 99.