International Mathematics (0607) | Statistical charts and diagrams

Welcome to Statistical Charts and Diagrams!

Hello there! This chapter is all about turning boring lists of numbers into beautiful, easy-to-understand visual representations. In statistics, raw data is often confusing, but charts and diagrams make it simple to spot trends, compare groups, and draw quick conclusions.
This skill is essential, not just for your IGCSE exam, but for interpreting information in the news, business, and science every single day. Let's learn how to draw and interpret these visual tools!

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1. Bar Charts and Diagrams (C10.6/E10.6(a))

Bar charts are perhaps the most common way to display data. They are generally used for discrete data or categorical data—data that can be counted or sorted into groups (like favourite colour or number of siblings).

Key Features of a Bar Chart

• Axis: The frequency (count) or value is shown on the vertical axis (y-axis). The categories or items are shown on the horizontal axis (x-axis).
• Bars: The height of each bar represents the frequency of that category.
• Gaps: Crucially, there must be a gap between the bars, because the data is discrete (the categories don't flow into one another, unlike in a histogram, which is not covered in this section).

Did you know? If you forget whether to put gaps in, remember this: If the categories are separate things (like "Apples" and "Bananas"), you separate the bars with a gap.

Types of Bar Charts Required in the Syllabus

Dual Bar Charts (Side-by-Side)

Dual bar charts (also called side-by-side bar charts) are fantastic for comparing two data sets within the same categories.
Example: Comparing the sales figures (Category: Months) of Product A (Bar 1) and Product B (Bar 2) right next to each other.

• Drawing Tip: Ensure you use a clear key (legend) to show which colour or pattern belongs to which data set (e.g., blue for boys, red for girls).

Composite Bar Charts (Stacked)

Composite bar charts (or stacked bar charts) show how the parts make up the total for each category.
Example: Showing the total number of students in each Year Group (Category: Year 10, Year 11), with the bar stacked to show how many are male and how many are female.

• Interpretation Tip: The total height of the stacked bar shows the overall total frequency for that category.

2. Pie Charts (C10.6/E10.6(b))

A pie chart (or circle chart) is used to show proportional data—how different components contribute to a total amount (100%).

The whole circle represents the total frequency, which is always \(360^\circ\).

Step-by-Step: Drawing a Pie Chart

To draw a pie chart, you must calculate the angle of the sector for each category.

1. Find the Total Frequency: Add up all the data values. Let the total be \(T\).
2. Calculate the Angle for each Category: The size of the angle must be proportional to the frequency.

   $$\text{Sector Angle} = \frac{\text{Frequency}}{\text{Total Frequency}} \times 360^\circ$$

3. Draw and Label: Use a protractor to accurately measure and draw the calculated angles in a circle. Label each sector clearly or use a key.

Memory Aid: Think of a pizza! Each topping (category) gets a slice (sector) proportional to how much pizza it takes up. Since a full circle is \(360^\circ\), you are essentially finding what fraction of \(360^\circ\) each category represents.

Common Mistake to Avoid: Make sure the sum of all your calculated angles equals exactly \(360^\circ\) (or very close, if rounding). If it doesn't, check your calculations!

3. Pictograms (C10.6/E10.6(c))

Pictograms (or pictographs) use pictures or symbols to represent frequency. They are often used for visual simplicity or in contexts where data needs to be easily accessible (e.g., primary school data, quick news reports).

Interpreting Pictograms

• The Key is Essential: You must look at the key first! The key tells you what one picture represents.
• Example: If a picture of a soccer ball represents 10 goals, then half a soccer ball represents 5 goals.
• Drawing Tip: Ensure the symbols are uniform in size. Only use fractions of the symbol if necessary, and these must clearly represent the fraction of the frequency (e.g., half a symbol for half the frequency).

4. Stem-and-Leaf Diagrams (C10.6/E10.6(d))

Stem-and-leaf diagrams are brilliant because they organise numerical data while still allowing you to see every original data point. They are particularly useful for displaying small to medium-sized sets of discrete or continuous data.

Parts of the Diagram

• Stem: This holds the leading digits (usually the tens, hundreds, or whole numbers). The stem usually reads vertically.
• Leaf: This holds the trailing digits (usually the ones or the first decimal place). The leaves read horizontally.

The Two Golden Rules (Syllabus Requirements!)

When you draw or interpret a stem-and-leaf diagram for your IGCSE exam, you MUST ensure two things:

1. It Must Be ORDERED: The leaves in each row (stem) must be arranged in numerical order (usually ascending, smallest to largest). If the data is not ordered, it is called an unordered stem-and-leaf diagram, and you must order it before final presentation.

2. It Must Have a KEY: The key explains what the stem and leaf digits represent. This is critical for knowing the actual value of the numbers.
Example Key: 2 | 5 means the number 25.

Example Key for Decimals: 10 | 3 means 10.3.

Step-by-Step Example

Data set: 12, 25, 15, 30, 21, 19, 32, 25.

Step 1: Unordered Diagram

1 | 2 5 9
2 | 5 1 5
3 | 0 2

Step 2: Ordered Diagram (This is what you must present!)

1 | 2 5 9
2 | 1 5 5
3 | 0 2

Key: 1 | 2 represents 12

Stem-and-leaf diagrams also help you quickly find the median and mode, as the data is already sorted!

5. Simple Frequency Distributions (C10.6/E10.6(e))

Although this sounds like a table (which it is!), the syllabus requires you to draw and interpret these. A simple frequency distribution is simply a structured table that summarises how often each value or category appears in a data set.

Structure of a Simple Frequency Table

These tables usually have three columns:

1. Category / Value (\(x\)): The actual data item (e.g., score, shoe size).
2. Tally: Used during data collection (groups of five marks: | | | | \(\text{/}\)).
3. Frequency (\(f\)): The total count for that category.

Importance: This table is the foundational step before creating most diagrams, like bar charts or pie charts.

Example:

Score (x)	Tally	Frequency (f)
1	| |	2
2	| | | | \(\text{/}\)	6
3	| | |	3

Interpreting Data from Tables and Charts (C10.2/E10.2)

Once you have created these charts, the next step is interpretation. This involves:

• Drawing Inferences: Making logical conclusions based on the visual evidence (e.g., "The bar chart shows that reading is the most popular hobby.")
• Comparing Sets: If using dual charts or comparing two different charts, discuss similarities, differences, and draw comparisons between averages (mean, median, mode) or spread (range).
• Appreciating Restrictions: Always remember that conclusions are based only on the given data. Do not draw wild, unsupported conclusions. (e.g., "We cannot conclude that everyone prefers reading, only the people surveyed.")

Final Key Takeaways for Charts

You need to master both drawing these charts (accurately, with labels, keys, and correct gaps/no gaps) AND reading information from them. Remember:

• Bar Charts: Gaps are essential. Use for counts of separate items.
• Pie Charts: Calculate angles based on the fraction of \(360^\circ\).
• Stem-and-Leaf: Must be ordered and have a key.

Keep practicing, and you'll find that statistics is less about complex formulas and more about clear, logical presentation!