What is Grouped Data?

S7-SA3-0047

Grade Level:

Class 12

AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics

Definition

What is it?

Grouped data is data that has been organized into categories or 'groups' based on certain intervals. Instead of looking at each individual data point, we count how many points fall into each group, making large datasets easier to understand.

Simple Example

Quick Example

Imagine you ask 50 students their marks out of 100 in a Maths test. Instead of listing all 50 individual marks, you can group them: 0-20 marks, 21-40 marks, 41-60 marks, 61-80 marks, and 81-100 marks. Then you just count how many students fall into each mark range.

Worked Example

Step-by-Step

Let's say we have the daily temperatures (in Celsius) for 15 days: 28, 31, 29, 30, 32, 27, 30, 29, 33, 28, 31, 29, 30, 32, 27.
---Step 1: Decide on the groups (also called 'class intervals'). Let's choose intervals of 2 degrees: 27-28, 29-30, 31-32, 33-34.
---Step 2: Go through each temperature and mark which group it belongs to.
---Step 3: Count how many temperatures fall into each group. For 27-28: 27, 28, 27, 28 (4 temperatures).
---Step 4: For 29-30: 29, 30, 30, 29, 29, 30 (6 temperatures).
---Step 5: For 31-32: 31, 32, 31, 32 (4 temperatures).
---Step 6: For 33-34: 33 (1 temperature).
---Answer: The grouped data is: 27-28 (4 days), 29-30 (6 days), 31-32 (4 days), 33-34 (1 day).

Why It Matters

Understanding grouped data helps scientists analyze large amounts of information quickly, from climate change patterns to patient responses to new medicines. Data scientists and engineers use this to make sense of complex systems, like how many people charge their EVs at different times or how many financial transactions happen in certain value ranges.

Common Mistakes

MISTAKE: Making class intervals overlap (e.g., 0-10 and 10-20) | CORRECTION: Ensure intervals are mutually exclusive (e.g., 0-10 and 11-20) or use conventions like [0, 10) and [10, 20) where 10 is included in the second interval.

MISTAKE: Not ensuring all data points are covered by the chosen intervals | CORRECTION: Check that the lowest and highest values in your raw data fall within your first and last class intervals respectively.

MISTAKE: Using too many or too few class intervals, making the data still hard to interpret | CORRECTION: Choose a reasonable number of intervals (usually 5-15) that effectively summarize the data without losing too much detail.

Practice Questions

Try It Yourself

QUESTION: A shopkeeper noted the number of customers visiting his shop each hour for 10 hours: 12, 15, 8, 20, 10, 18, 13, 16, 9, 14. Group this data into intervals of 5, starting from 5-9. | ANSWER: 5-9 (2 customers), 10-14 (4 customers), 15-19 (3 customers), 20-24 (1 customer).

QUESTION: For the data set: 5, 12, 18, 25, 30, 32, 38, 45, 48, 50. If the class intervals are 0-10, 11-20, 21-30, 31-40, 41-50, create the grouped frequency distribution. | ANSWER: 0-10 (1), 11-20 (2), 21-30 (2), 31-40 (2), 41-50 (3).

QUESTION: The heights (in cm) of 20 plants are: 10, 12, 15, 11, 18, 20, 22, 13, 16, 19, 21, 14, 17, 23, 25, 24, 10, 12, 15, 18. Create a grouped frequency table using class intervals of size 5, starting from 10-14. | ANSWER: 10-14 (7 plants), 15-19 (7 plants), 20-24 (5 plants), 25-29 (1 plant).

MCQ

Quick Quiz

Which of the following is NOT a characteristic of good class intervals for grouped data?

They should cover all data points.

They should be of equal width.

They should overlap with each other.

They should be mutually exclusive (no overlap).

The Correct Answer Is:

Good class intervals should never overlap, meaning a data point should only belong to one interval. Overlapping intervals (Option C) would make it unclear where to place certain data points.

Real World Connection

In the Real World

When you see reports about rainfall in different regions of India, or how many people use a certain mobile network in different age groups, that's often based on grouped data. For example, the Indian Meteorological Department (IMD) groups daily temperatures or rainfall into ranges to show climate patterns across the country.

Key Vocabulary

Key Terms

CLASS INTERVAL: A range of values used to group data. | FREQUENCY: The number of data points that fall within a specific class interval. | UNGROUPED DATA: Raw data that has not been organized into groups. | RANGE: The difference between the highest and lowest values in a dataset.

What's Next

What to Learn Next

Now that you understand grouped data, the next step is to learn about 'Frequency Distribution Tables'. This will show you how to formally present grouped data and prepare it for further analysis, like drawing graphs.