What is 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.
FAQs on Frequency Distribution: Concept and Applications
1. What are frequency distributions?
A frequency distribution is a way of organizing data to show how often each value or range of values occurs in a dataset. It provides a clear summary of the data by listing possible values alongside their frequencies. This approach helps reveal patterns, trends, and distributions within the data, making analysis much easier. By using a frequency distribution, you can quickly determine where most values fall and identify any outliers. This technique is especially useful in statistics for both categorical and numerical data.
2. What is an example of a frequency distribution?
A frequency distribution can be illustrated using test scores from a class. Suppose 20 students scored between 60 and 100 on an exam. The data can be organized into score ranges, such as 60–69, 70–79, 80–89, and 90–100, and the number of students in each range is counted. For example, if 3 students scored 60–69, 7 scored 70–79, 6 scored 80–89, and 4 scored 90–100, these counts form the frequency distribution. This table format allows teachers to see which score ranges are most common and evaluate the overall performance statistically.
3. What are the 4 types of frequency distribution?
Frequency distributions can be classified into four main types, each based on how the values are organized or the type of data involved. These include:
- Ungrouped Frequency Distribution: Lists each individual value and its frequency.
- Grouped Frequency Distribution: Groups data values into intervals or classes.
- Cumulative Frequency Distribution: Shows the running total of frequencies up to each class or value.
- Relative Frequency Distribution: Expresses frequencies as a proportion or percentage of the total.
Each type serves different purposes in data analysis and helps understand patterns in both raw and summarized data sets.
4. How to generate a frequency distribution?
Constructing a frequency distribution involves systematic steps to organize your data. The process helps visualize how values are spread out in a dataset.
- Collect Data: List all data values from your dataset.
- Determine Intervals: Decide on class intervals if using grouped data.
- Tally Frequencies: Count the number of occurrences for each value or interval.
- Create the Table: Arrange the results in a table showing values or intervals and their corresponding frequencies.
This method is commonly used in descriptive statistics and can be applied to both qualitative and quantitative data for clear analysis.
5. Why is a frequency distribution important in statistics?
A frequency distribution is crucial in statistics because it organizes large amounts of data in a meaningful way. By showing how often each value or range appears, it highlights patterns such as central tendency, outliers, and data dispersion. This helps statisticians make informed decisions, compare different data sets, and visualize data through charts or graphs. In summary, frequency distributions provide the foundation for further statistical analysis and interpretation.
6. What is the difference between grouped and ungrouped frequency distributions?
The main distinction between grouped and ungrouped frequency distributions lies in how the data is organized. In ungrouped frequency distributions, each unique data value is listed along with its frequency, suitable for small datasets with limited unique values. Grouped frequency distributions, on the other hand, organize values into intervals or classes (e.g., 10–19, 20–29), which is ideal for larger datasets or when values spread widely. Grouping makes it easier to spot overall trends and patterns when dealing with complex or lengthy data.
7. How do you interpret a frequency distribution table?
Interpreting a frequency distribution table involves examining how data values are distributed across different categories or intervals. Start by identifying which classes or values have the highest and lowest frequencies; these indicate where most data points fall and any potential outliers. Look for clusters, gaps, or patterns that reveal the dataset’s shape and spread. By analyzing this table, you can quickly assess trends, draw comparisons, and make informed decisions based on the underlying data structure.
8. What is the purpose of a cumulative frequency distribution?
A cumulative frequency distribution displays the sum of frequencies for all classes up to a specific point, providing insight into how values accumulate within a dataset. This approach helps determine how many observations fall below or within a given interval. Cumulative distributions are useful when analyzing percentiles or medians, as they allow for easy calculation of cumulative proportions. In statistical studies, this format is commonly used to understand relative standing or trends across data ranges.
9. How can frequency distributions be visualized graphically?
Frequency distributions can be effectively visualized through various graphs, making it easier to interpret and communicate data patterns. Common graphical methods include:
- Histogram: Uses bars to represent frequency for numerical intervals.
- Bar Chart: Shows frequencies for categorical data.
- Frequency Polygon: Connects data points with lines for a smooth distribution display.
- Ogive: Visualizes cumulative frequencies, typically for percentiles or medians.
Visual representations enhance understanding by clearly showing the distribution and shape of the data.
10. What is relative frequency and how is it calculated?
Relative frequency shows how often a value or category appears in comparison to the total number of observations. To calculate relative frequency, divide the frequency of a specific value by the overall total number of data points. For example, if a value occurs 5 times in a set of 50 observations, its relative frequency is 5/50 = 0.10 (or 10%). Relative frequency distributions help compare data more easily, especially when dealing with different sample sizes.
11. When should you use a frequency distribution?
A frequency distribution is most useful when you need to summarize and analyze raw data, especially if the dataset is large or contains many repeated values. It helps when comparing categories, identifying common or rare items, and detecting patterns. Use it when creating histograms, bar graphs, or preparing data for further statistical calculations. Overall, frequency distributions are a vital first step in exploratory data analysis for both qualitative and quantitative data.
12. What are some limitations of frequency distributions?
While frequency distributions are powerful tools for summarizing data, they have certain limitations. They can mask individual data details, especially in grouped distributions, where information about specific values is lost. The choice of interval size in grouped distributions can also influence interpretation, potentially obscuring true data patterns. Additionally, frequency distributions are less effective with very small datasets or continuous variables that require fine detail. Recognizing these limits helps ensure accurate and meaningful data analysis.
