Introduction

Raw data collected from experiments, surveys, or observations is often difficult to understand at first glance. A long list of numbers may contain useful information, but patterns are not always obvious. Before analysing data, it is important to organise it into a clear and systematic form.

One of the most useful ways to organise data is with frequency tables. These tables show how often different values or groups of values occur, making it much easier to identify patterns, compare results, and prepare data for graphs and statistical calculations.

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Why Organise Data?

Organising data helps us:

• Find patterns.
• Compare results.
• Identify unusual values.
• Reduce errors.
• Prepare data for graphs and statistical analysis.

Well-organised data is easier to understand and communicate.

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Figure 1. Organising raw data into tables makes patterns easier to identify.

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Raw Data

Raw data is data collected in its original, unorganised form.

Example:

18, 16, 20, 18, 17, 19, 18, 16, 20, 17, 18, 19

Although the information is complete, it is difficult to see which values occur most often.

Organising the data makes interpretation much easier.

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Frequency Tables

A frequency table lists each value and the number of times it occurs.

Example

The frequency is simply the number of times each value appears.

Frequency tables work well for small datasets or discrete data.

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Constructing a Frequency Table

To create a frequency table:

1. List all the different values in order.
2. Count how many times each value occurs.
3. Record the frequencies.
4. Check that the total frequency equals the number of data values collected.

Organising values in ascending order makes the table easier to read.

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Figure 2. A frequency table summarises how often each value occurs.

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Grouped Frequency Tables

Large datasets are often organised into groups, called class intervals.

Instead of listing every individual value, similar values are grouped together.

Example

Grouped frequency tables make large datasets much easier to summarise.

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Choosing Class Intervals

Good class intervals should:

• Cover all data values.
• Be equal in width whenever possible.
• Not overlap.
• Be easy to interpret.

For example:

✔ 0–9, 10–19, 20–29

✘ 0–10, 10–20, 20–30

The second example overlaps because the value 10 belongs to two groups.

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Cumulative Frequency Tables

A cumulative frequency table shows the running total of frequencies.

Example

The cumulative frequency tells us how many observations are at or below each value.

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Figure 3. Cumulative frequency tables show the running total of observations.

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Interpreting Organised Data

Organised data helps answer questions such as:

• Which value occurs most often?
• What is the smallest value?
• What is the largest value?
• How many observations are below a certain value?
• Are there any unusual values?

Looking for patterns becomes much easier once the data has been organised.

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Preparing Data for Analysis

Before calculating averages or drawing graphs, data should be checked.

Good preparation includes:

• Removing obvious recording errors.
• Checking for missing values.
• Ensuring units are consistent.
• Organising values into tables.
• Labelling headings clearly.

Well-prepared data leads to more reliable analysis.

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Choosing the Right Table

Choosing the appropriate table makes the data easier to interpret.

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Figure 4. Different types of frequency tables are suited to different types of datasets.

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Why Organising Data Is Important

Scientists and statisticians organise data because it:

• Reveals patterns.
• Simplifies calculations.
• Makes graphs easier to construct.
• Improves communication.
• Reduces mistakes.

Organised data provides the foundation for all statistical analysis.

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Figure 5. Organised data is the starting point for graphs, averages, and statistical analysis.

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Worked Example

Question

The following test scores were recorded:

15, 17, 18, 16, 18, 17, 19, 18, 20, 17

Construct a frequency table.

Solution

The total frequency is 10, which matches the number of scores collected.

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Real-World Connection

Schools often organise examination results into frequency tables before analysing student performance. A grouped frequency table can quickly show how many students scored within different mark ranges, while a cumulative frequency table helps identify the percentage of students who achieved a particular grade or higher. This information supports teachers in evaluating class performance and planning future lessons.

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Did You Know?

Before computers became common, statisticians organised thousands of data values by hand using tally marks. Even today, tally marks remain a quick and effective way to record frequencies during classroom experiments, surveys, and field investigations before transferring the data into frequency tables.

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Key Terms

Class interval – A range of values used in a grouped frequency table.

Cumulative frequency – The running total of frequencies up to and including a given value or class.

Cumulative frequency table – A table showing frequencies and their running totals.

Frequency – The number of times a value or group of values occurs.

Frequency table – A table showing each value and its frequency.

Grouped frequency table – A frequency table in which values are organised into class intervals.

Raw data – Data in its original, unorganised form.

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Key Takeaways

• Raw data should be organised before it is analysed.
• A frequency table shows how often each value occurs and is suitable for smaller datasets.
• A grouped frequency table summarises larger datasets by placing values into class intervals.
• A cumulative frequency table shows the running total of observations and is useful for determining how many values fall below a given point.
• Organised data makes patterns easier to identify and prepares the data for graphs and statistical calculations.
• Careful organisation improves the accuracy, clarity, and usefulness of statistical investigations.