How to Make a Frequency Distribution Table Step-by-Step
The concept of frequency distribution plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding frequency distribution helps students quickly organize, interpret, and analyze data in a systematic and visual manner.
What Is Frequency Distribution?
A frequency distribution is a way of organizing raw data into a table or chart that shows how often each value (or group of values) appears in a dataset. You’ll find this concept applied in areas such as statistics, data handling, and mathematical analysis. Frequency distribution is especially useful for seeing patterns and identifying trends in data at a glance.
Types of Frequency Distribution
There are several ways to classify frequency distributions:
- Ungrouped Frequency Distribution: Each unique value in the data is listed with its frequency. Best for small datasets or categorical data.
- Grouped Frequency Distribution: Data is divided into intervals (called class intervals) and frequencies are counted for each interval. Useful for large datasets or continuous data.
- Cumulative Frequency Distribution: Shows the running total of frequencies up to each point.
- Relative Frequency Distribution: Shows frequency as a proportion or percentage.
| Type | When Used | Example |
|---|---|---|
| Ungrouped | Small or simple datasets | Number of students scoring exact marks |
| Grouped | Large numeric data with ranges | Heights divided in ranges (150-155, 156-160) |
Key Formula for Frequency Distribution
Here are some standard formulas for frequency distribution:
- Frequency: Number of times a value appears in a set.
- Relative Frequency: Relative Frequency = (Frequency of a class) / (Total number of observations)
- Cumulative Frequency: Sum of the current frequency and all previous frequencies
- Class Mark: Class Mark = (Lower Limit + Upper Limit) ÷ 2
Cross-Disciplinary Usage
Frequency distribution is not only useful in Maths but also plays an important role in Physics, Computer Science, and daily logical reasoning. Students preparing for JEE, NEET, or board exams will find frequency tables, histograms, and related data handling topics regularly in exam questions.
Step-by-Step Illustration
Let’s make an ungrouped frequency distribution table for this data set (marks out of 10): 6, 8, 6, 10, 8, 9, 7, 10, 7, 6
| Marks | Frequency |
|---|---|
| 6 | 3 |
| 7 | 2 |
| 8 | 2 |
| 9 | 1 |
| 10 | 2 |
Now for a grouped frequency table, let’s say marks out of 20: 5, 8, 12, 14, 17, 19, 9, 15, 12, 11, 18, 6, 13, 12, 7
| Marks Interval | Frequency |
|---|---|
| 5-9 | 5 |
| 10-14 | 6 |
| 15-19 | 4 |
Step-by-step for creating a grouped frequency distribution table:
1. Arrange the data in ascending order.2. Decide the number and width of class intervals.
3. Create columns for class intervals and tally marks.
4. Go through each data point and place a tally mark where it fits.
5. Count the tallies and write the frequency for each class.
Speed Trick or Vedic Shortcut
A quick trick for tallying large datasets: Instead of going line-by-line, first arrange numbers in order. Next, mark repeated numbers at once and tick off as you add to the frequency. This avoids missing counts and saves precious time, especially during exams. Vedantu’s live sessions cover many such tally and grouping techniques for data handling speed.
Try These Yourself
- Construct a frequency distribution table for the data: 11, 12, 12, 13, 14, 11, 13, 13, 15, 12.
- Make a grouped frequency table for heights (cm): 154, 159, 160, 165, 167, 155, 167, 162, 160, 156 using intervals of 5.
- Find the cumulative frequency for the grouped data: 5-9 (4), 10-14 (6), 15-19 (3).
- Convert the frequency table into a bar graph or histogram.
Frequent Errors and Misunderstandings
- Choosing incorrect class interval width for grouped data.
- Overlapping intervals (e.g., 10-15 and 15-20) which may double-count or omit values.
- Missing values in tally marks or skipping data when counting frequencies.
- Confusing frequency and cumulative frequency columns.
Relation to Other Concepts
The idea of frequency distribution connects closely with topics such as histogram, frequency polygon, and data handling. Mastering frequency tables helps you easily solve questions on averages, mode, median, and other vital statistics covered in later chapters.
Classroom Tip
A quick way to remember frequency tables: Always check that the total frequency matches the total number of data values. For grouped tables, ensure there are no gaps or overlaps between intervals. Vedantu’s teachers suggest sketching quick bar graphs from the table for easier visualization during practice or tests.
Wrapping It All Up
We explored frequency distribution—from definition, formulas, examples, mistakes, and its link with other maths concepts. Practice regularly with Vedantu’s resources to get comfortable with organizing and analyzing data, which is a must-have skill for maths success and competitive exams.
Explore More on Data and Statistics:
FAQs on Frequency Distribution: Meaning, Table Construction & Solved Examples
1. What is a frequency distribution in Maths?
A frequency distribution is a table that displays how often different outcomes or values appear in a dataset. It organises raw data into a more understandable format, showing the frequency (count) of each value or group of values. For example, it can show how many students scored in a particular range of marks on a test.
2. How do you construct a frequency distribution table step-by-step?
To construct a frequency distribution table, follow these steps:
- Step 1: Determine the Range: Find the highest and lowest values in your dataset to calculate the range.
- Step 2: Decide on Class Intervals: If it's a large dataset, divide the range into a suitable number of non-overlapping class intervals (e.g., 0-10, 11-20).
- Step 3: Tally the Data: Go through your dataset and make a tally mark for each value in its corresponding class interval.
- Step 4: Count the Frequencies: Count the tally marks for each interval to find the frequency. The sum of all frequencies must equal the total number of data points.
3. What are the main types of frequency distributions?
There are two primary types of frequency distributions:
- Ungrouped Frequency Distribution: This lists each individual value in the dataset along with its frequency. It is best suited for datasets with a small number of unique values.
- Grouped Frequency Distribution: This groups the data into class intervals or bins. It is used for large datasets or continuous data to simplify analysis and spot trends more easily.
Other related types include cumulative and relative frequency distributions.
4. Why is choosing the right class interval width so important in a grouped frequency distribution?
Choosing the right class interval width is crucial because it directly affects the interpretation of the data. If the intervals are too wide, important details and patterns might be hidden. If they are too narrow, the table can become too long and complex, making it difficult to see the overall trend. A well-chosen interval provides a clear, balanced summary of the data's distribution.
5. What are the key formulas associated with a frequency distribution table?
The main formulas you will encounter when working with frequency distributions as per the CBSE curriculum for 2025-26 are:
- Range: Highest Value – Lowest Value
- Class Mark (or Mid-point): (Upper Limit + Lower Limit) / 2
- Relative Frequency: Frequency of a class / Total number of observations
- Cumulative Frequency: The sum of a class's frequency and all frequencies of the classes before it.
6. What is the difference between a histogram and a frequency polygon?
Both are graphical representations of a frequency distribution, but they differ in their appearance and use. A histogram uses adjacent rectangular bars to show the frequency of data in each class interval, with no gaps between the bars. A frequency polygon is a line graph formed by joining the mid-points of the tops of the bars in a histogram. It is useful for comparing multiple distributions on the same graph.
7. How do cumulative frequency and relative frequency help in analysing data differently?
They offer different perspectives on the data:
- Cumulative Frequency tells you the running total. It answers questions like, "How many students scored less than 50 marks?" It's about accumulation and totals up to a certain point.
- Relative Frequency shows proportion or percentage. It answers questions like, "What percentage of students scored between 80 and 90?" It helps compare the distribution across datasets of different sizes.
8. Can a frequency distribution table be used for non-numerical data?
Yes, absolutely. A frequency distribution table is very effective for categorical data (non-numerical data like colours, types of animals, or favourite subjects). Instead of class intervals, the table lists each category, and the frequency column shows how many times each category appears in the dataset. For example, a table could show the frequency of different blood types in a group of people.
9. What are some real-world applications of frequency distribution?
Frequency distribution is used in many real-world fields to make sense of data. For example:
- In business, to analyse sales data for different products.
- In hospitals, to track the number of patients with different illnesses.
- In meteorology, to record the frequency of certain temperature ranges over a month.
- In schools, to understand the distribution of marks among students in an exam.
10. How does a frequency distribution help in identifying patterns or outliers in a dataset?
A frequency distribution, especially when visualised as a histogram, makes it easy to see the shape of the data. You can quickly identify where most of the data points are clustered (the mode), whether the data is symmetric, or if it is skewed. Outliers, which are values that are unusually high or low compared to the rest of the data, will appear as isolated bars far from the main group, making them easy to spot.
