Score Distribution Summary Statistics

  • Raw Score: Number correct (adjusted by weighting/scoring formula if used)
  • Frequency: Number of students obtaining that raw score
  • Cumulative Frequency: Number of students obtaining that raw score or lower
  • Percentile Rank: Percent correct corresponding to that raw score
    Standard Score: A linear transformation of that raw score to a distribution with a mean of 50 and a standard deviation of 10. This scale is useful if you wish to combine two or more tests that are unequal in difficulty. Consult Testing Office for a fuller explanation before using this procedure.
  • Number of Questions: total number of questions on the test.
  • Number of Omissions in Key: number of items left blank on the key
  • Number of Keyed Questions: number of items actually scored.
  • Number of Students: number of answer sheets computer reads.
    Sum of Scores: sum of the raw scores obtained by each student (used to compute the variance and standard deviation).
  • Sum of Squared Scores: sum of the squared raw scores obtained from each student (used to compute the variance and standard deviation).
  • Mean: the average score, calculated by dividing the sum of scores by the number of examinees.
  • Median: the middle raw score of the distribution; 50 percent of the obtained raw scores are higher and 50 percent are lower than the median.
  • Variance: the average of the squared deviations of the raw scores from the mean.
  • Standard Deviation: the square root of the variance. If the distribution of scores is normal, approximately two-thirds of the scores will fall within one standard deviation above and below the mean.
  • Kuder Richardson Reliability (KR-20): a measure of response consistency across all items. KR-20 will usually range from about .20 to about .95. A high KR-20 means that the test or subtest can be considered as a homogeneous pool of items having a common focus.
  • Standard Error of Measurement (S.E.M.): a measure of the reliability of any raw score. The S.E.M. yields an estimate of the range of raw score values within which a student's "true" score is likely to fall.

Score Distrubition