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Frequency distribution

A frequency distribution is a list of the values that a variable takes in a sample. Most frequently it is a list, ordered by quantity, showing the number of times each value appears. For example, if 100 people rate a five-point attitude item assessing their agreement with a statement on a scale on which 1 denotes strong agreement and 5 strong disagreement, the frequency distribution of their responses might look like:

Rating Degree of agreement n
1 Strongly agree 25
2 Agree somewhat 35
3 Not sure 20
4 Disagree somewhat 15
5 Strongly disagree   5

Statistical hypothesis testing is founded on the assessment of differences and similarities between frequency distributions. This assessment involves measures of central tendency or averages, such as the mean and median, and measures of variability or statistical dispersion, such as the standard deviation or variance.

A frequency distribution is said to be skewed when its mean and median are different. The kurtosis of a frequency distribution is the concentration of scores at the mean, or how peaked the distribution appears if depicted graphically for example, in a histogram. If the distribution is more peaked than the normal distribution it is said to be leptokurtic; if less peaked it is said to be platykurtic.