A frequency distribution is commonly represented in tabular format and can summarize data for either categorical or numerical variables. Frequency distribution tables are organized so that the data is classified into a certain number of categories and the number of units pertaining to each category is recorded. Numerical distributions are used for numerical variables, in which the variables are measured according to size. On the other hand, categorical distributions organize variables with reference to a particular attribute or quality.^{1}

When compiling data for a frequency distribution table, the first step involves detailing the number of categories which are required and then, it is necessary to decide upon class limits. Class limits, is a term which refers to the need to evaluate the boundaries for each category with regards to what category it follows and which category it proceeds^{1}. Once the class limits are determined, the next step involves counting the individual observations and tallying the counts for each category. It is in this step that the class frequencies are deciphered. ^{1}

Frequency distributions have a plethora of applications in statistics. For example, frequency distributions can be graphed to determine whether or not the data follows a normal distribution. Histograms are typically constructed when testing for normality because it is clear to determine whether data is skewed or not using these figures. As well, frequency distributions can be used for hypothesis testing and during the assessment of data, such as when calculating measures of central tendency. Essentially, the main objective of frequency distributions is to summarize data in a clear and concise manner and considering their commonality in statistics, learning to construct and interpret them is a critical skill.

Reference:

1. Walpole, R., Myers, R., Myers, S. and Ye, K. (2011). Probability and Statistics for Engineers. 8th ed. Prentice Hall.

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