Frequency Distribution

Before jumping to frequency distribution, let us first understand what frequency is. Frequency refers to a measure of how often something has happened. The frequency of any observation tells you the repeated number of times a specific observation occurs in the observed data. Tables can show both qualitative and quantitative variables; qualitative variables are also known as categorical and represent different non-measurable categories like eye colour, brands, etc., while quantitative variables are numeric. 

In a frequency distribution, we use class intervals to represent a range of values in the data under consideration. The intervals are framed concerning the minimum and maximum value between certain thresholds. A major difference between a frequency distribution series and a frequency distribution table is that most often in a frequency distribution series, the x-variable is discrete numeric, whereas, in a frequency distribution table, it is used for continuous values. 

The different types of frequency distributions are ungrouped frequency distributions, grouped frequency distributions, cumulative frequency distributions, and relative frequency distributions.

Grouped Frequency Distribution: Sometimes to derive insights from an observation easily, we group them into class intervals. 

• Calculate the maximum and minimum value of the data set

• Divide this range by the number of groups you intend to have in your analysis

• Segregate the data within this small sub-group basis the class width

• Calculate the frequency of data within each group 

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Ungrouped Frequency Distribution: The ungrouped cumulative distribution is similar to grouped frequency distribution except for the fact that class intervals are not created, and values are ordered from minimum to maximum. 

• List the unique values as the first column.

• Calculate the repeated instances of each unique value and record it

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Cumulative Frequency Distribution

When you add or subtract the frequencies of all the previous class intervals to determine the frequency of a particular class interval, it results in a cumulative frequency distribution. Also, another major difference is that class intervals do not denote a range but instead represent a logical conclusion like greater than a threshold value or less than a threshold value. 

• Calculate frequencies for every category

• Arrange in ascending or descending order according to categories/class intervals based on whether one wants to prepare an increasing/decreasing cumulative frequency distribution

• Total all the preceding frequencies. E.g., the second category's frequency is calculated by the sum of the first and second category's individual frequencies. Third is calculated by the sum of the first, second, third category's individual frequencies 

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Relative Frequency Distribution

A relative frequency distribution is extensively used in our day-to-day statistical applications, which refers to the proportion of total observations associated with each category. It is calculated for individual class intervals by dividing them by the total observed frequencies. Relative frequencies can be written as a percentage, fraction, or decimal points. Cumulative relative frequency is the total of all preceding relative frequencies. To find the cumulative relative frequency, total all the previous relative frequencies till the current category.

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Common Representations of Frequency Distributions

The most common way in which a frequency distribution is visualised is using a bar chart. People also use pie charts for their data analysis of frequency distributions. The major advantage of these representations is that one can get a clear idea of the distribution with a glance. However, the disadvantage is that there is a chance of outliers getting lost in these representations if we are not careful. In the real world, analysts commonly use frequency distributions to identify how data is skewed and where the focus should lie on.

Solved Examples: 

A research was done in 20 homes in Chennai Avadi. People were asked how many bikes they own?  The results were: 1, 4, 3, 0, 5, 1, 2, 2, 1, 5, 2, 3, 2, 2, 0, 1, 2, 0, 3, 2. 

Present this data in the Frequency Distribution Table. Also, find the maximum number of homes owning the same number of bikes.

Solution: Divide the number of bikes in every home into different intervals. Every house can own either 0,1,2,3, etc. bikes. All these numbers form the rows. Now calculate the number of homes having {0,1,2,3, etc.} bikes. This is called the frequency. When you plot this in the form of a table: 

It can be seen from the table that 6 homes have 2 bikes and a lesser number of people own other numbers of bikes. Hence the answer is 6 homes.

Did You Know?

Toyota used Frequency Distributions for its famous Assembly line manufacturing and discovery of a lean process. 

Many noted automobile manufacturers use this method to identify the root cause of machine failure. Using this method, all possible causes of the frequency of failure of each of these causes was plotted. By this, we can identify which reason is the highest contributor to machine failure, and immediate actions can be taken to resolve it.

Frequency distribution comes under the statistical branch of mathematics. It is an extremely important concept that is usually taught in earlier classes, starting from The 8th grade. It is important in the sense that it helps in organising data in a systematic manner which helps in easier analysis.

To make the learning process fun and easier the Vedantu‘s team has curated study material related to frequency distribution. This article mainly deals with the many types of frequency distribution and how we can construct a frequency distribution table. This article explains in-depth about grouped frequency distribution, and grouped frequency distribution, cumulative frequency distribution, relative frequency distribution. For students to get a good hold over the concept Vedantu’s team has also provided practice questions along with their solutions so that students can keep checking their progress and Study in a systematic manner. This article simplifies frequency distribution with the use of simple examples.

Frequency distribution covers the statistical part of mathematics. It helps in the collection, organisation, distribution, and interpretation of data. It helps to analyse and understand what a certain dataset reveals about a particular topic. It is helpful as it interprets data which is useful while conducting research or while studying a particular discipline. Tables represent both qualitative and quantitative variables; qualitative variables are also known as categorical and represent different non-measurable categories like eye colour, brands, etc., while quantitative variables are numeric.

Frequency can be defined as the number of times a certain event occurs. If in a particular research a certain number occurs more than once then we can say that its frequency happens to be more than once. After writing down the different frequencies in a table students can get a frequency distribution table. Basically, it means to lay out data in a systematic manner which is based on the number of observations. It helps to analyse and present data in a systematic manner.

In order to understand and get a clear grasp over the concept of frequency distribution students should be well informed about certain things that are used in frequency distribution such as classes, class limits, the midpoint of each class, the magnitude of a class interval, class frequency.

Data becomes extremely difficult to organise when it is present in large numbers. With the help of a frequency distribution table students or researchers can get a better understanding of the research conducted. They can interpret the data according to their needs.