Frequency Distribution Table Frequency Distribution Table In statistics, a frequency distribution is an arrangement of the values that one or more variables take in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of values in the sample. Univariate frequency tables Univariate frequency distributions are often presented as lists ordered by quantity showing the number of times each value appears. For example, if 100 people rate a five-point Likert scale 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: Rank

Degree of agreement

1 2 3 4 5

Strongly agree Agree somewhat Not sure Disagree somewhat Strongly disagree

Number 20 30 20 15 15

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A different tabulation scheme aggregates values into bins such that each bin encompasses a range of values. For example, the heights of the students in a class could be organized into the following frequency table.\ Height range 4.5–5.0 feet 5.0–5.5 feet 5.5–6 feet 6.0–6.5 feet

Number of students 25 35 20 20

Cumulative number 25 60 80 100

A frequency distribution shows us a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data e.g. to show results of an election, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc. Some of the graphs that can be used with frequency distributions are histograms, line graphs, bar charts and pie charts. Frequency distributions are used for both qualitative and quantitative data. Managing and operating on frequency tabulated data is much simpler than operation on raw data. There are simple algorithms to calculate median, mean, standard deviation etc. from these tables. 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.

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Relative Frequency Distribution A relative frequency distribution is a distribution in which relative frequencies are recorded against each class interval. Relative frequency of a class is the frequency obtained by dividing frequency by the total frequency. Relative frequency is the proportion of the total frequency that is in any given class interval in the frequency distribution. Relative Frequency Distribution Table If the frequency of the frequency distribution table is changed into relative frequency then frequency distribution table is called as relative frequency distribution table. For a data set consisting of n values. If f is the frequency of a particular value then the ratio 'fn' is called its relative frequency.

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