Details of Normal Distribution
- Curve is symmetrical
- Measure of central tendency is at center of the distribution; its peak
- Central Tendency (CT) is a point
- Measure of dispersion is standard deviation (SD) and is the distance from the central tendency to the inflection point (where the normal curve changes from being concave downward to concave upwards)
- Standard Deviation is a length (not a point).
- A normal curve is a normal curve because certain proportion of cases fall within certain ranges of standard deviations.
- Memorize: about 1/3 of cases fall between the mean and 1 SD above the mean; 68% or about 2/3 of cases fall between 1 SD below the mean to 1 SD above the mean; 96% of cases fall within 2 SDs of the mean; virtually all cases fall within 3 SDs of the CT.
- A normal curve is defined by telling its central tendency and standard deviation:
- A variable is distributed normally with a particular CT and particular SD
- X ~ N(CT, SD)
- X ~N(µ, [sigma])
- Stanford-Binet IQ ~ N(100, 15)
Memorize the following information
- About 2/3 (68%) of all cases are within 1 standard deviation from the mean
- 96% of all cases are within 2 standard deviations from the mean
- Virtually all cases fall within 3 standard deviations from the mean.
Note: Prints on one page at 80%.
© 2002 by BurrtonWoodruff. All rights reserved. Modified Sunday, March 25, 2007