What is a Frequency Table?

S3-SA3-0018

Grade Level:

Class 8

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

Definition

What is it?

A frequency table is a way to organise raw data by showing how often each value or item appears in a dataset. It lists different categories or values and their 'frequency,' which means how many times each one occurs.

Simple Example

Quick Example

Imagine your teacher asked all 30 students in your class what their favourite fruit is. Instead of just a long list like 'Mango, Apple, Banana, Mango, Apple...', a frequency table would quickly show you how many students like Mango, how many like Apple, and how many like Banana.

Worked Example

Step-by-Step

Let's say a shopkeeper noted down the number of 'samosas' sold each hour for 5 hours: 12, 15, 12, 18, 15. Let's create a frequency table for this data.

STEP 1: Identify all the unique values in the data. The unique values are 12, 15, and 18.
---STEP 2: For each unique value, count how many times it appears in the original data.
---STEP 3: For '12', it appears 2 times.
---STEP 4: For '15', it appears 2 times.
---STEP 5: For '18', it appears 1 time.
---STEP 6: Create a table with two columns: 'Number of Samosas Sold' and 'Frequency (Number of Hours)'.
---STEP 7: Fill in the table:
Number of Samosas Sold | Frequency
----------------------|-----------
12 | 2
15 | 2
18 | 1
---Answer: The frequency table clearly shows that 12 samosas were sold in 2 hours, 15 samosas in 2 hours, and 18 samosas in 1 hour.

Why It Matters

Frequency tables are the first step in understanding large amounts of data, like election results or customer feedback. Data scientists use them to quickly spot patterns, while engineers might use them to analyse how often a machine part needs replacement. They help in making smart decisions.

Common Mistakes

MISTAKE: Missing a data point while counting frequency. | CORRECTION: Always double-check your total frequency count against the total number of data points you started with. They should match!

MISTAKE: Not listing all unique values in the table. | CORRECTION: Go through your raw data carefully and list every single unique item or number that appears, even if its frequency is 1.

MISTAKE: Confusing the value itself with its frequency. | CORRECTION: Remember, the 'value' is what you are counting (e.g., 'Mango'), and 'frequency' is HOW MANY times it appeared (e.g., '5 students').

Practice Questions

Try It Yourself

QUESTION: A survey asked students how many siblings they have: 0, 1, 2, 1, 0, 3, 1, 2, 0, 1. Create a frequency table. | ANSWER: Siblings | Frequency
----------|----------
0 | 3
1 | 4
2 | 2
3 | 1

QUESTION: The marks obtained by 10 students in a math test (out of 10) are: 7, 8, 5, 7, 9, 8, 7, 6, 8, 7. Make a frequency table for these marks. | ANSWER: Marks | Frequency
-------|----------
5 | 1
6 | 1
7 | 4
8 | 3
9 | 1

QUESTION: A call center recorded the number of calls handled per hour by an agent over 6 hours: 10, 12, 10, 15, 12, 10. Also, find the total number of calls handled. | ANSWER: Calls Handled | Frequency
---------------|----------
10 | 3
12 | 2
15 | 1
Total calls handled = (10 * 3) + (12 * 2) + (15 * 1) = 30 + 24 + 15 = 69 calls.

MCQ

Quick Quiz

Which of the following best describes the 'frequency' in a frequency table?

The type of data being counted

The total number of categories

How many times a particular value or item appears

The biggest value in the data set

The Correct Answer Is:

Frequency specifically means 'how often' or 'how many times' something occurs. Options A, B, and D describe other aspects of data or tables, not the definition of frequency itself.

Real World Connection

In the Real World

When you see cricket match statistics showing 'boundaries hit by each batsman,' that's often based on frequency counting. Or, imagine a delivery app like Swiggy or Zomato tracking which food items are ordered most frequently in a city to decide what to stock more of. This helps businesses understand customer preferences and manage inventory efficiently.

Key Vocabulary

Key Terms

DATA: A collection of facts, numbers, or information. | FREQUENCY: The number of times a particular value or item occurs in a dataset. | RAW DATA: Data collected in its original, unorganized form. | CATEGORY: A distinct group or type of item.

What's Next

What to Learn Next

Now that you understand frequency tables, you're ready to learn about 'Grouped Frequency Tables' and 'Bar Graphs.' These concepts build on frequency tables to help you organise and visualise even larger datasets, making data analysis even more powerful!