# Frequency Distribution

The systematic representation of data, arranged to demonstrate data falling within certain ranges, classes, or categories, is called a frequency distribution.

When data is presented in a frequency distribution, the objective is to show the number of times a particular value, or range of values, occurs. Graphs are frequently used to illustrate frequency distributions. Common forms of frequency distribution are the histogram, bar graph, line graph, frequency polygon, and the frequency curve, which associates a quantitative value (the frequency) with each range, class, or category of data.

A cumulative frequency distribution is a representation in which each successive division includes all of the items in previous divisions: The last division includes all of the data in the entire distribution. A probability distribution is similar to a frequency distribution; however, in a probability distribution the probability of occurrence is associated with each range, class, or category. The sum of the probabilities in a probability distribution is one, while the sum of the frequencies in a frequency distribution is the total number of data items.

Abnormal frequency distributions are termed skewed distributions. In a skewed distribution curve, the tails surrounding the apex of the distribution curve are unequal, with one tail much smaller (containing fewer cases) than the number of cases on the other side of the apex or maximum. Depending on where the more normal or gradual tail is located, distribution graphs may be described as being skewed to the left or to the right.

KEY TERMS

Bell curve—
A frequency distribution in the shape of a bell. In a normal bell curve there is a peak in the middle of the distribution graph and smoothly diminishing tails that fall off equally on both sides of the apex of the curve.
Skewed distribution—
A distribution curve where the tails to the left or right of the apex of the distribution curve (the top of the bell shape) are unequal, with one tail much smaller (containing fewer cases) than the number of cases on the other side of the apex.

See also Significance level ; Statistical significance ; Statistics in psychology .

## Resources

BOOKS

Altman, Douglas G. Statistics with Confidence: Confidence Intervals and Statistical Guidelines. London: BMJ Books, 2011.

Der, Geoff, and Brian Everitt. A Handbook of Statistical Analyses Using SAS. Boca Raton, FL: CRC Press, 2009.

Freedman, David. Statistical Models: Theory and Practice. Cambridge, UK: Cambridge University Press, 2009.

Hastie, Trevor, et al. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. New York: Springer, 2009.

Mukhopadhyay, Parimal. Multivariate Statistical Analysis. Singapore: World Scientific, 2009.

Privitera, Gregory J. Statistics for the Behavioral Sciences. Thousand Oaks, CA: SAGE, 2012.

Spiegel, Murray R., et al. Probability and Statistics. New York: McGraw-Hill, 2009.

Stapleton, James H. Linear Statistical Models. Hoboken, NJ: Wiley, 2009.

PERIODICALS

Cioffi-Revilla, Claudio. “Computational Social Science.” Computational Statistics 2, no. 3 (May/June 2010): 259–71.

WEB SITES

Science.gov. “Statistics.” http://www.science.gov/browse/w_113I7.htm (accessed September 19, 2015).

Science.gov. “Studies and Statistics.” http://www.science.gov/browse/w_133B.htm (accessed September 19, 2015).

World Health Organization. “Data and Statistics.” http://www.who.int/research/en/ (accessed September 19, 2015).

World Health Organization. “Statistics.” http://www.who.int/topics/statistics/en (accessed September 19, 2015).