Numbers. Numbers mean different things in different situations. Consider three answers that appear to be identical but are not. “What number were you wearing in the race?” “5” What place did you finish in ?” “5” How many minutes did it take you to finish?” “5”. Number Scales. Nominal Scale
The arithmetic average of a distribution of scores; most generally used measure of central tendency.
Score that represents the exact middle of the distribution; the fiftieth percentile; the score that 50% of the scores are above and 50% of the scores are below.
Score that occurs most frequently; may have more than one mode.
Least used measure of central tendency.
Not used for additional statistics.
Not affected by extreme scores.
Determined by subtracting the lowest score from the highest score; represents on the extreme scores.
1. Dependent on the two extreme scores.
2. Least useful measure of variability.
Formula: R = Hx - Lx
1. Is the square root of the variance, which is the average of the squared deviations from the mean. Population variance is represented as F2 and the sample variance is represented as s2.
2. Is applicable to interval and ratio data, includes all
scores, and is the most reliable measure of variability.
3. Is used with the mean. In a normal distribution, one
standard deviation added to the mean and one standard
deviation subtracted from the mean includes the middle
68.26% of the scores.