Collection and representation of data: tables, charts, diagrams, histograms, scatter diagrams

Why do we collect data?

Imagine you’re a detective 🕵️‍♂️ trying to solve a mystery. The clues you gather are like data points. The more clues you have, the clearer the picture of the mystery becomes. In maths, we collect data to find patterns, make predictions, and answer questions about the world.

Data can be qualitative (e.g., colours, types) or quantitative (numbers, measurements).

• Qualitative: “What colour is your favourite shirt?”
• Quantitative: “How many minutes do you study each day?”

When collecting data, remember the sampling method – are you looking at everyone (a census) or just a few (a sample)?

Tables arrange data neatly. Think of a table as a tidy bookshelf where each book (data point) has a specific place.

Charts turn numbers into visuals, making patterns easier to spot.

• Bar Chart – good for comparing categories.
• Pie Chart – shows parts of a whole.
• Line Graph – shows change over time.

Example: If you want to see how many students prefer each subject, a bar chart would be perfect.

Histograms group quantitative data into class intervals (like age groups).

Suppose we have the following scores: 55, 62, 68, 73, 78, 84, 91, 95.

We might group them into intervals: 50–60, 61–70, 71–80, 81–90, 91–100.

Count how many scores fall into each interval and draw bars accordingly.

Analogy: Think of a histogram as a set of shelves where each shelf holds books (scores) that belong to the same height range.

A scatter diagram plots two quantitative variables to see if they are related.

Example: Plotting study hours (x-axis) against exam scores (y-axis).

Look for a trend: if points rise together, there might be a positive relationship.

Analogy: Imagine a seesaw – if one side goes up, the other side goes down. A scatter diagram helps you see if that’s happening.

Tip 1: Always check the units when reading data.

Tip 2: For tables, double‑check that rows and columns match the question’s requirements.

Tip 3: When drawing a histogram, ensure all intervals are of the same width unless specified.

Tip 4: In scatter diagrams, look for a clear trend before deciding on a line of best fit.

Given the following data set of daily study times (in minutes): 30, 45, 60, 45, 90, 30, 60, 75, 45, 60, 30, 90, 60, 45, 30.

1. Construct a frequency table.
2. Draw a histogram.
3. Identify the mode.

Try to solve it before checking the answer on the next page!