# Normal Curve

Living reference work entry

First Online:

**DOI:**https://doi.org/10.1007/978-1-4614-6435-8_1745-3

## Synonyms

## Definition

The normal curve represents the shape of an important class of statistical probabilities (see Fig. 1 below). The normal curve is used to characterize complex constructs containing continuous random variables. Many phenomena observed in nature have been found to follow a normal distribution. Some human attributes such as height, weight, intelligence, and even social skills can be said to be normally distributed. For example, most people’s height clusters around the population mean, and an equally small proportion of people are represented at either extreme end of the distribution. When represented graphically, the resulting shape resembles that of a bell where there is a single peak at the mean, while the tails extend to the right and left into infinity. Thus, the probability of being 5′10″ is relatively high, while the probability of being 7′4″ is much smaller. Raw data from any number of disciplines can be transformed into

*standard scores*using a simple formula. Once scores have been standardized, the mean of the curve = 0 and the standard deviation = 1. This is referred to as the*standard normal distribution*. Performance on most major standardized tests of intelligence produces standardized scores defined as IQ score and reflects a population mean of 100 and a standard deviation of 15 points. The normal curve is the most prominent probability distribution model used in statistics and psychometrics.All normal distributions comply with the following postulates:

68% of all scores fall within + or − 1 SD from the M.

95% of all scores fall within + or − 2 SD from the M.

99% of all scores fall within + or − 3 SD from the M.

## See Also

## References and Reading

- Anastasi, A., & Urbina, S. (1997).
*Psychological testing*(7th ed.). Upper Saddle River: Prentice-Hall.Google Scholar - Aron, A., Aron, E. N., & Coups, E. J. (2008).
*Statistics for psychology*(5th ed.). Upper Saddle River: Pearson Prentice Hall.Google Scholar - Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003).
*Applied multiple regression/correlation analysis for the behavioral sciences*(3rd ed.). Mawah: Lawrence Erlbaum Associates.Google Scholar - Gregory, R. J. (2004).
*Psychological testing: History, principles, and applications*(4th ed.). Boston: Allyn and Bacon.Google Scholar - Keppel, G., & Wickens, T. D. (2004).
*Design and analysis: A researcher’s handbook*(4th ed.). Upper Saddle River: Pearson Prentice Hall.Google Scholar

## Copyright information

© Springer Science+Business Media LLC 2018