What is a Grouped Frequency Table?

S1-SA4-0947

Grade Level:

Class 5

Data Science, Computing, AI, Statistics, Science

Definition

What is it?

A Grouped Frequency Table is a way to organize a lot of data by putting similar values into 'groups' or 'intervals'. Instead of listing every single value, we count how many values fall into each group. This makes large datasets much easier to understand and look at.

Simple Example

Quick Example

Imagine your teacher records the marks of 50 students in a maths test. Instead of listing all 50 marks one by one, a grouped frequency table would show how many students scored between 0-20, how many between 21-40, and so on. This quickly tells you if most students scored high or low.

Worked Example

Step-by-Step

Let's say a shop noted down the ages of 15 customers who bought a new mobile phone:
12, 25, 30, 18, 45, 22, 38, 15, 28, 50, 33, 19, 27, 40, 35

Step 1: Decide the groups (or 'class intervals'). Let's use groups of 10 years: 10-20, 21-30, 31-40, 41-50.
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Step 2: Go through each age and put a tally mark ( | ) in the correct group.
12 (10-20) | 25 (21-30) | 30 (21-30) | 18 (10-20) | 45 (41-50) | 22 (21-30) | 38 (31-40) | 15 (10-20) | 28 (21-30) | 50 (41-50) | 33 (31-40) | 19 (10-20) | 27 (21-30) | 40 (31-40) | 35 (31-40)
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Step 3: Count the tally marks for each group to find the frequency.

Age Group | Tally Marks | Frequency
----------|-------------|-----------
10-20 | |||| | 4
21-30 | ||||| | 5
31-40 | |||| | 4
41-50 | || | 2

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Step 4: Check if the total frequency matches the total number of data points (4 + 5 + 4 + 2 = 15, which is correct).

Answer: The grouped frequency table shows how many customers fall into each age group.

Why It Matters

Understanding grouped frequency tables is a first step into Data Science and Statistics. It helps you quickly make sense of large amounts of information, just like how cricket analysts use it to see batsman scores or how scientists group experiment results. This skill is key for anyone working with data, from market researchers to AI engineers.

Common Mistakes

MISTAKE: Overlapping class intervals like 0-10 and then 10-20, making it unclear where a value like '10' goes. | CORRECTION: Make sure intervals do not overlap, for example: 0-10 and then 11-20. Or use 'less than' (e.g., 0 to less than 10, 10 to less than 20).

MISTAKE: Not including all data points in the table or missing the highest/lowest values when setting up intervals. | CORRECTION: Always check the minimum and maximum values in your data first. Ensure your groups cover the entire range of data.

MISTAKE: Unequal class sizes (e.g., 0-5, then 6-20, then 21-25). | CORRECTION: For a clear and fair comparison, try to keep the width of each class interval the same (e.g., 0-10, 11-20, 21-30).

Practice Questions

Try It Yourself

QUESTION: The heights (in cm) of 10 plants are: 15, 22, 18, 25, 30, 20, 16, 28, 23, 19. Create a grouped frequency table using class intervals 15-20, 21-26, 27-32. | ANSWER:
Height Group | Frequency
------------|-----------
15-20 | 5
21-26 | 3
27-32 | 2

QUESTION: A survey asked 20 students how many hours they spend studying per week: 5, 8, 12, 7, 10, 6, 9, 15, 11, 8, 13, 7, 10, 6, 14, 9, 12, 8, 11, 7. Make a grouped frequency table with class intervals of 5 hours (e.g., 5-9, 10-14, 15-19). | ANSWER:
Hours Studied | Frequency
--------------|-----------
5-9 | 11
10-14 | 8
15-19 | 1

QUESTION: A local bus service recorded the number of passengers on 25 trips: 28, 35, 19, 42, 30, 25, 38, 22, 45, 33, 29, 36, 21, 40, 31, 26, 39, 23, 41, 34, 27, 32, 24, 37, 43. Create a grouped frequency table using 4 equal class intervals. | ANSWER:
(One possible answer with intervals of 6 passengers, starting from 19)
Passengers | Frequency
-----------|-----------
19-24 | 5
25-30 | 6
31-36 | 7
37-42 | 5
43-48 | 2

MCQ

Quick Quiz

Which of these is the main reason to use a Grouped Frequency Table?

To list every single data point individually.

To make small datasets look bigger.

To organize large amounts of data into manageable groups for easier understanding.

To always find the exact average of all data points.

The Correct Answer Is:

Option C is correct because grouped frequency tables are designed to simplify large datasets by grouping data, making them easier to read and interpret. Options A and B are incorrect as they go against the purpose, and D is incorrect because you can't find the exact average from grouped data, only an estimate.

Real World Connection

In the Real World

Grouped frequency tables are used everywhere! For example, when the Indian Meteorological Department (IMD) shows rainfall data, they might group cities by rainfall ranges (e.g., 0-50mm, 51-100mm) to easily compare regions. E-commerce websites like Flipkart use it to show how many products fall into different price ranges (e.g., under Rs. 500, Rs. 501-1000) to help customers find what they need.

Key Vocabulary

Key Terms

FREQUENCY: The number of times a particular value or item appears in a dataset. | CLASS INTERVAL: The range of values that make up a group in a grouped frequency table (e.g., 10-20). | CLASS SIZE/WIDTH: The difference between the upper and lower limits of a class interval. | DATA: A collection of facts, such as numbers, words, measurements, or observations.

What's Next

What to Learn Next

Great job learning about grouped frequency tables! Next, you can explore how to represent this data visually using 'Histograms'. Histograms are special bar graphs that directly use the groups from your frequency table to show patterns in data even more clearly.