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Frequency tables can be useful for describing the number of occurrences of a particular type of datum within a dataset. Frequency tables, also called frequency distributions, are one of the most basic tools for displaying descriptive statistics. Frequency tables are widely utilized as an at-a-glance reference into the distribution of data; they are easy to interpret and they can display large data sets in a fairly concise manner. Frequency tables can help to identify obvious trends within a data set and can be used to compare data between data sets of the same type. Frequency tables aren't appropriate for every application, however. They can obscure extreme values (more than X or less than Y), and they do not lend themselves to analyses of the skew and kurtosis of the data.

## Rapid Data Visualization

Frequency tables can quickly reveal outliers and even significant trends within a data set with not much more than a cursory inspection. For example, a teacher might display students' grades for a midterm on a frequency table in order to get a quick look at how her class is doing overall. The number in the frequency column would represent the number of students receiving that grade; for a class of 25 students, the frequency distribution of letter grades received might look something like this: Grade Frequency A..............7 B.............13 C..............3 D..............2

## Visualizing Relative Abundance

Frequency tables can help researchers to examine the relative abundance of each particular target data within their sample. Relative abundance represents how much of the data set is comprised of the target data. Relative abundance is often represented as a frequency histogram, but can easily be displayed in a frequency table. Consider the same frequency distribution of midterm grades. Relative abundance is simply the percentage of the students who scored a particular grade, and can be helpful for conceptualizing data without overthinking it. For example, with the added column that displays the percent occurrence of each grade, you can easily see that more than half of the class scored a B, without having to scrutinize the data in much detail.

Grade Frequency Relative Abundance (% frequency) A..............7..............28% B.............13............52% C..............3.............12% D..............2..............8%

## Complex Data Sets May Need Classed Into Intervals

One disadvantage is that it is difficult to comprehend complex data sets that are displayed on a frequency table. Large data sets can be divided into interval classes for easy visualization using a frequency table. For example, if you asked the next 100 people you see what their age was, you would likely get a wide range of answers spanning anywhere from three to ninety-three. Rather than including rows for every age in your frequency table, you could classify the data into intervals, such as 0 - 10 years, 11 - 20 years, 21 - 30 years and so on. This may also be referred to as a grouped frequency distribution.

## Frequency Tables Can Obscure Skew and Kurtosis

Unless displayed on a histogram, skewness and kurtosis of data may not be readily apparent in a frequency table. The skewness tells you which direction your data tends towards. If grades were displayed across the X-axis of a graph showing the frequency of midterm grades for our 25 students above, the distribution would skew toward the A's and B's. Kurtosis tells you about the central peak of your data -- whether it would fall in line of a normal distribution, which is a nice smooth bell curve, or be tall and sharp. If you graph the midterm grades in our example, you will find a tall peak at B with a sharp dropoff in the distribution of lower grades.