Frequency Distribution in Statistics Explained
Published by at November 14th, 2025 , Revised On November 14, 2025
What Is Frequency Distribution
A frequency distribution provides a clear picture of how data values are spread across a dataset. It shows patterns, trends, and data organisation by indicating how frequently each observation occurs.
This helps researchers quickly identify concentrations of data, detect anomalies, and understand the overall shape of the data distribution.
In statistics, frequency distribution acts as a bridge between raw data and meaningful analysis. When data are simply listed, it can be difficult to interpret. When the data is organised into a frequency table, patterns become more visible. This structured representation helps in both descriptive and inferential analysis.
An example of frequency distribution in everyday data could be the number of hours students spend studying each day. If most students study between 2 and 3 hours, that interval will have the highest frequency.
Types Of Frequency Distribution
A frequency distribution can take several forms depending on how the data are presented and analysed. The main types include
- Ungrouped
- Grouped
- Cumulative
- Relative
Ungrouped Frequency Distribution
An ungrouped frequency distribution displays individual data values along with their corresponding frequencies. It is typically used when the dataset is small and values do not need to be combined into ranges or intervals.
Example: If five students score 4, 5, 6, 5, and 7 in a quiz, the ungrouped frequency distribution simply lists each score and how many times it occurs.
Ungrouped distributions are ideal for small or precise datasets where individual data points are meaningful and easy to analyse without grouping.
Grouped Frequency Distribution
A grouped frequency distribution is used when dealing with a large dataset. In this method, data are divided into class intervals, ranges of values that summarise multiple observations.
Example: If you have exam scores ranging from 0 to 100, you might create class intervals such as 0-10, 11-20, and so on. Each interval’s frequency shows how many scores fall within that range.
In order to form class intervals:
- Identify the smallest and largest data values.
- Decide on the number of classes.
- Determine the class width (range ÷ number of classes).
This approach simplifies analysis and reveals data trends more clearly, especially in large-scale research.
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Cumulative Frequency Distribution
A cumulative frequency distribution shows the running total of frequencies up to a certain point in the dataset. It helps researchers understand how data accumulate across intervals and is particularly useful for identifying medians, quartiles, and percentiles.
Example: If class intervals represent ages (10-19, 20-29, 30-39), the cumulative frequency of 30-39 includes all individuals aged 10-39.
A cumulative frequency table provides a quick overview of how many observations fall below or within a particular class range, supporting deeper statistical analysis.
Relative Frequency Distribution
A relative frequency distribution expresses each class’s frequency as a proportion or percentage of the total number of observations. It shows how frequently a category occurs relative to the whole dataset, making it valuable for comparative analysis.
How to calculate relative frequency
Relative Frequency = Class Frequency / Total Frequency
For example, if 10 out of 50 students scored between 70-80, the relative frequency for that class is 10 ÷ 50 = 0.2 (or 20%).
This type of distribution is beneficial in comparing datasets of different sizes and is widely used in data visualisation, probability studies, and business analytics.
Components Of A Frequency Distribution Table
A frequency distribution table organises raw data into a structured form. Here are the key components
| Class Intervals | These represent the data ranges or groups into which values are divided. Each interval should be mutually exclusive and collectively exhaustive. |
|---|---|
| Frequency | This shows the number of observations that fall within each class interval. It helps identify the most common data ranges. |
| Cumulative Frequency | This is the running total of frequencies as you move down the table. It is useful for identifying medians and percentiles. |
| Relative and Percentage Frequency | These express frequencies as proportions or percentages of the total number of observations. |
| Tally Marks and Symbols | Tally marks are often used to count occurrences before converting them into numerical frequencies. They serve as a visual aid during manual data collection. |
How To Construct A Frequency Distribution Table
Here is a step-by-step guide to help you build one manually and in Excel.
Step 1: Choose Class Intervals
- Identify the smallest and largest values in your dataset.
- Decide how many classes you need (usually 5-10 for clarity).
- Calculate class width using the formula:
Class Width = (Highest Value – Lowest Value) / Number of Classes
Step 2: Arrange Data into Groups
Create non-overlapping intervals (e.g., 0-10, 11-20, 21-30). You have to make sure that the intervals cover the full data range.
Step 3: Calculate Frequency
Count how many data points fall into each class interval, and record the counts in the frequency column.
Step 4: Compute Cumulative and Relative Frequency
- Add each frequency progressively to get cumulative totals.
- Divide each class frequency by the total to find relative frequency.
Step 5: Example Dataset for Practice
| Class Interval | Frequency (f) | Cumulative Frequency (CF) | Relative Frequency (RF) |
|---|---|---|---|
| 0-10 | 4 | 4 | 0.20 |
| 11-20 | 6 | 10 | 0.30 |
| 21-30 | 5 | 15 | 0.25 |
| 31-40 | 5 | 20 | 0.25 |
| Total | 20 | – | 1.00 |
In Excel:
- Enter raw data in one column.
- Use the FREQUENCY() function or Pivot Tables to automatically generate frequency counts.
- Insert formulas to calculate cumulative and relative frequencies.
Visual Representation Of Frequency Distribution
A frequency distribution graph helps illustrate how values are spread across categories or intervals. When visualising frequency distribution, always label axes clearly, use consistent scales, and highlight key patterns or peaks.
Below are the main types:
- Histograms: Show frequencies using adjacent bars, where each bar represents a class interval. Ideal for continuous data and visualising skewness or symmetry.
- Frequency Polygons: Formed by connecting the midpoints of histogram bars with straight lines, highlighting the shape of the data distribution.
- Bar Charts and Pie Charts: Suitable for categorical or discrete data. They visually compare frequencies and proportions between groups.
Frequency Distribution In Excel & SPSS
Modern researchers often rely on statistical software to generate frequency distributions quickly and accurately. Two of the most commonly used tools are Microsoft Excel and SPSS (Statistical Package for the Social Sciences).
Frequency Distribution In Excel
Excel offers several built-in features for creating a frequency distribution table efficiently.
- Enter your raw data in one column.
- In a second column, define class intervals (bins).
- Use the FREQUENCY() function to calculate how many data points fall within each bin.
=FREQUENCY(data range, bins range)
- Press Ctrl + Shift + Enter to generate results.
- Use formulas to calculate cumulative and relative frequencies if needed.
You can also use Pivot Tables:
- Go to Insert → PivotTable → Select your data range.
- Drag the variable to the Rows field and again to the Values field.
- Change “Value Field Settings” to “Count” to display frequency.
Excel’s Insert Chart feature allows you to create histograms, bar charts, or frequency polygons.
Frequency Distribution In SPSS
SPSS provides a quick, automated way to create frequency tables using the Descriptive Statistics tool.
- Open your dataset in SPSS.
- Click on Analyse → Descriptive Statistics → Frequencies.
- Move the desired variable into the “Variables” box.
- Click OK to generate a table showing frequencies, percentages, cumulative percentages, and valid cases.
The output includes both frequency tables and visual charts (such as bar graphs or histograms), allowing for quick interpretation of results. SPSS also provides additional descriptive statistics like mean, median, and mode within the same interface.
Example Interpretation
If 60% of respondents rate satisfaction as “High” and 10% as “Low,” the frequency distribution indicates that the majority of participants perceive a positive experience.
Frequently Asked Questions
A frequency distribution is a way of organising data to show how often each value or range of values occurs in a dataset. It helps researchers identify patterns, trends, and variations within data, making analysis easier and more meaningful.
The four main types are ungrouped, grouped, cumulative, and relative frequency distributions. Each type presents data differently depending on the dataset’s size and purpose, from raw counts to cumulative and percentage-based formats.
To create a frequency distribution table, list all data values or class intervals, count how many times each occurs (frequency), and record totals. You can do this manually or use tools like Excel’s FREQUENCY() function or SPSS’s Descriptive Statistics feature for automated tables.
Frequency refers to the number of times a value appears in a dataset, while relative frequency shows that number as a proportion or percentage of the total. Relative frequency helps compare data categories on the same scale.
To calculate cumulative frequency, add each frequency progressively as you move down the list of class intervals. It shows how data accumulate over a range and is useful for finding medians, quartiles, and percentiles.
In Excel, use the FREQUENCY() function or a Pivot Table to count data occurrences across intervals. Then, add columns for cumulative and relative frequencies. You can also create a histogram using the Insert → Chart option for quick visualisation.
In SPSS, go to Analyse → Descriptive Statistics → Frequencies, select your variable, and click OK. SPSS will automatically create a frequency table with counts, percentages, and cumulative percentages, along with optional graphs.
Frequency distribution is crucial because it simplifies large volumes of data, reveals patterns, and supports statistical analysis. It forms the basis for descriptive and inferential statistics.
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