What is a Frequency Distribution Table for Grouped Data?

S3-SA3-0230

Grade Level:

Class 8

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

A Frequency Distribution Table for Grouped Data is a way to organize a large set of numbers into smaller groups called 'classes' or 'intervals'. It shows how many times (frequency) numbers fall within each of these groups, making it easier to understand patterns in the data.

Simple Example

Quick Example

Imagine your teacher wants to show marks of 50 students in a math exam (out of 100). Instead of listing all 50 marks, she can group them: 0-20 marks, 21-40 marks, 41-60 marks, etc. Then, she counts how many students scored in each group. This organized list is a frequency distribution table for grouped data.

Worked Example

Step-by-Step

Let's create a frequency distribution table for the daily earnings (in Rupees) of 20 auto-rickshaw drivers:
250, 310, 280, 400, 350, 290, 320, 380, 260, 300, 330, 360, 270, 340, 390, 315, 295, 370, 305, 355.

Step 1: Decide on class intervals. Let's use intervals of 50: 250-300, 301-350, 351-400.
---Step 2: Go through each earning and mark a tally in the correct interval.
For 250: 250-300 |
For 310: 301-350 |
For 280: 250-300 ||
...and so on.
---Step 3: Count the tallies for each interval to find the frequency.
Interval: 250-300 | Tallies: ||||| || (7 drivers)
Interval: 301-350 | Tallies: ||||| ||| (8 drivers)
Interval: 351-400 | Tallies: ||||| (5 drivers)
---Step 4: Create the table.

Earning (Rs) | Tally Marks | Frequency
---------------------------------------
250-300 | ||||| || | 7
301-350 | ||||| ||| | 8
351-400 | ||||| | 5
---------------------------------------
Total | | 20

Answer: The frequency distribution table clearly shows that most drivers earned between 301-350 Rupees.

Why It Matters

This concept helps us make sense of huge amounts of information, like understanding how many people use a certain app or how many students score in different mark ranges. It's used in data science to analyze trends, in economics to study income groups, and even in AI/ML to categorize data for learning.

Common Mistakes

MISTAKE: Overlapping class intervals like 0-10, 10-20, 20-30. If a value is 10, it could go into two groups. | CORRECTION: Make sure intervals are non-overlapping. For example, 0-10, 11-20, 21-30, or 0-10 (where 10 is excluded), 10-20 (where 20 is excluded).

MISTAKE: Not including all data points in any class interval. | CORRECTION: Ensure your chosen class intervals cover the entire range from the smallest to the largest value in your data set.

MISTAKE: Using inconsistent class widths (e.g., 0-10, then 11-30, then 31-35). | CORRECTION: For most simple grouped frequency tables, keep the width of all class intervals the same for easier comparison and analysis.

Practice Questions

Try It Yourself

QUESTION: The ages of 15 people attending a local festival are: 12, 18, 25, 30, 15, 22, 28, 35, 10, 20, 32, 14, 26, 38, 17. Create a frequency distribution table with class intervals 10-20, 21-30, 31-40. | ANSWER:
Age Group | Frequency
----------------------
10-20 | 7
21-30 | 5
31-40 | 3

QUESTION: A shop recorded the number of mobile recharges done per day for 20 days: 15, 22, 18, 30, 25, 17, 28, 32, 20, 23, 19, 26, 31, 24, 16, 29, 21, 33, 14, 27. If the class intervals are 10-15, 16-20, 21-25, 26-30, 31-35, what is the frequency for the 21-25 interval? | ANSWER: 5

QUESTION: The heights (in cm) of 20 plants are: 12.5, 15.0, 11.8, 13.2, 16.1, 14.7, 12.9, 15.5, 10.5, 13.8, 16.5, 11.2, 14.1, 12.0, 15.8, 10.9, 13.5, 16.0, 14.5, 12.3. Create a frequency distribution table with class intervals of width 2 cm, starting from 10.0-11.9. What is the total frequency? | ANSWER:
Height (cm) | Frequency
-----------------------
10.0-11.9 | 4
12.0-13.9 | 8
14.0-15.9 | 6
16.0-17.9 | 2
Total Frequency: 20

MCQ

Quick Quiz

Why do we use a Frequency Distribution Table for Grouped Data?

To list every single data point separately

To make data harder to understand

To organize large data into manageable groups and see patterns

To only show the smallest and largest values

The Correct Answer Is:

Option C is correct because the main purpose of grouping data is to simplify large datasets, making it easier to identify trends and patterns. Options A, B, and D do not reflect the primary benefit.

Real World Connection

In the Real World

When cricket analysts study player performance, they might group runs scored into intervals like 0-25, 26-50, 51-75, etc., to see how often a batsman scores big. Similarly, e-commerce companies like Flipkart or Amazon group customer ages or spending habits to understand their target audience better and offer relevant products.

Key Vocabulary

Key Terms

FREQUENCY: The number of times a particular value or item appears in a dataset | CLASS INTERVAL: A range of values used to group data in a frequency distribution table | TALLY MARKS: Vertical lines used to count frequencies, usually in groups of five | UNGROUPED DATA: Raw data that has not been organized into classes or intervals

What's Next

What to Learn Next

Now that you understand how to group data, you can learn about 'Histograms'. Histograms are visual graphs that use bars to show the information from a grouped frequency distribution table, making patterns even easier to spot. Keep exploring!