Data Representation • Topic 1 of 3

Collection of Data and Frequency Tables

What is Data?

Data is a collection of facts, numbers, or information gathered for analysis. Examples include test scores, heights of students, number of pets in a family, or daily temperatures.

Types of Data:

Type	Definition	Example
Primary Data	Collected directly by the user	Conducting a survey in your class
Secondary Data	Taken from already published sources	Using census data from a website

Collection of Data:

Data can be collected through:

Surveys - Asking questions to people
Experiments - Conducting tests
Observations - Watching and recording
Questionnaires - Written forms to fill out
Interviews - One-on-one questioning

What is a Frequency Table?

A frequency table organizes data by showing how many times each value (or range of values) occurs. The number of times a value appears is called its frequency.

Steps to Create a Frequency Table:

List all distinct values (or class intervals) in one column
Use tally marks to count occurrences
Count the tallies and write the frequency
Add a total row at the bottom

Tally Marks Chart:

Number	Tally Marks
1	\
2	\	\
3	\	\	\
4	\	\	\	\
5	~~\	\	\	\	~~
6	~~\	\	\	\	~~ \

Grouped Frequency Table:

When data has many different values, we group them into class intervals (ranges). Example: 0-10, 11-20, 21-30, etc.

Real-life Example: A teacher records the number of books read by 20 students in a month: 3, 5, 2, 3, 4, 5, 3, 2, 4, 3, 5, 2, 3, 4, 5, 3, 2, 4, 3, 5. A frequency table helps see how many students read each number of books.

Solved Examples

Worked Example

The marks obtained by 20 students in a maths test (out of 10) are: 7, 8, 6, 7, 9, 7, 8, 6, 7, 8, 9, 7, 6, 8, 7, 9, 7, 8, 6, 7. Prepare a frequency table.

Solution

Step 1: Identify distinct values: 6, 7, 8, 9
Step 2: Count occurrences using tally marks
Step 3: Marks 6: appears 4 times → ||||
Step 4: Marks 7: appears 8 times → |||| ||||
Step 5: Marks 8: appears 5 times → |||| |
Step 6: Marks 9: appears 3 times → |||
Step 7: Create table:

Marks	Tally Marks	Frequency
6	\	\	\	\		4
7	\	\	\	\	\	\	\	8
8	\	\	\	\	\		5
9	\	\	\		3
Total		20

Answer: Frequency table prepared as above.

Worked Example

The ages (in years) of 15 children in a club are: 10, 12, 11, 10, 13, 11, 12, 10, 11, 12, 13, 10, 11, 12, 11. Find the frequency of each age and determine which age appears most often.

Solution

Step 1: List distinct ages: 10, 11, 12, 13
Step 2: Count frequency:
Age 10: appears 4 times
Age 11: appears 5 times
Age 12: appears 4 times
Age 13: appears 2 times
Step 3: Age 11 appears most frequently (mode = 11)

Answer: Frequencies: 10→4, 11→5, 12→4, 13→2. Most frequent age: 11 years.

Worked Example

The weights (in kg) of 30 students are given below. Create a grouped frequency table with class intervals 30-34, 35-39, 40-44, 45-49, 50-54. Weights: 32, 38, 42, 45, 51, 33, 39, 44, 47, 52, 34, 37, 41, 46, 50, 35, 40, 43, 48, 53, 36, 38, 42, 45, 49, 31, 39, 44, 46, 52.

Solution

Step 1: List class intervals: 30-34, 35-39, 40-44, 45-49, 50-54
Step 2: Count weights in each interval:
30-34: 32, 33, 34, 31 → 4 students
35-39: 38, 39, 37, 35, 36, 38, 39 → 7 students
40-44: 42, 44, 41, 43, 40, 42, 44 → 7 students
45-49: 45, 47, 46, 45, 48, 46, 49 → 7 students
50-54: 51, 52, 50, 53, 52 → 5 students
Step 3: Verify total: 4 + 7 + 7 + 7 + 5 = 30 ✓

Answer: Grouped frequency table created with frequencies: 30-34:4, 35-39:7, 40-44:7, 45-49:7, 50-54:5.

Key Points

Data is collected information used for analysis
Primary data = collected directly; Secondary data = from existing sources
Frequency = number of times a value occurs in the data set
Tally marks help count frequencies efficiently (groups of 5)
Frequency table organizes data showing values and their frequencies
Grouped frequency table groups data into class intervals for large data sets
Total frequency should equal the total number of observations

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.Data that is not organised is called:

Explanation: Raw data.

Q2.The frequency is the number of times a value:

Explanation: Occurs.

Q3.Tally marks are usually grouped in sets of:

Explanation: Five.

Q4.The range is the highest value minus the:

Explanation: Lowest value.

Practice more MCQs → 📝 Assignment · 35 marks