IB MYP 3 Mathematics 9.1 Collecting, Classifying, Organising and Representing Data Study Notes - New Syllabus

9.1 – Collecting, Classifying, Organising and Representing Data

Statistics is the process of collecting, organising, representing, analysing and interpreting data. Data helps us answer questions and make decisions about people, objects, events or situations.

A statistical investigation usually follows a logical process:

What Is Data?

Data is a collection of facts, measurements, observations or information. A single piece of data is called a datum.

Examples of data include:

• the heights of students
• the favourite sports of students
• the number of goals scored in a match
• the temperature recorded each day
• the colours of cars in a car park

Population and Sample

The population is the complete group that we are interested in studying. A sample is a smaller part of the population that is selected for investigation.

Census and Sample

A census collects information from every member of the population. A sample investigation collects information from only part of the population.

Bias in Data Collection

Bias occurs when the method used to collect data tends to favour certain results. A biased sample may not represent the population fairly.

For example, suppose a school wants to know whether students like the new school lunch. If the school asks only students who are eating the new lunch, the results may not represent all students.

 Classifying Data

Data can be classified according to the type of information it contains. Two important types are categorical data and numerical data.

Tally and Frequency Tables

A frequency tells us how many times a particular value or category occurs. A tally is a quick way of counting observations. Groups of five are commonly used when making tally marks.

The total frequency tells us the total number of observations:

\( \text{Total frequency} = \text{number of observations} \)

Representing Categorical Data

Categorical data can be represented using several types of graphs.

Pie Charts

A pie chart represents a whole circle of \(360^\circ\). The angle of each sector depends on the fraction or percentage of the data in that category.

\( \text{Sector angle} = \frac{\text{frequency}}{\text{total frequency}} \times 360^\circ \)

If a category represents \(25\%\) of the data:

\( \text{Sector angle} = 25\% \times 360^\circ = 90^\circ \)

 Line Graphs

A line graph is useful when the data values have a natural order, especially when showing how something changes over time. The points are plotted and then connected with straight line segments.

For a line graph:

• Give the graph a clear title.
• Label both axes.
• Include suitable units.
• Choose an appropriate scale.
• Plot each point accurately.
• Join consecutive points when appropriate.

 Choosing the Correct Representation

Reading and Interpreting Graphs

When interpreting a graph, do not simply state a number. Explain what the number means in the context of the problem.

For example, instead of writing:

\( 18 \)

write:

\( \text{18 students chose basketball.} \)

Misleading Graphs

Graphs can sometimes give a misleading impression if they are poorly designed. Common problems include:

• using a vertical axis that does not start at zero when comparison of bar heights is important;
• using unequal intervals on an axis;
• leaving out labels or units;
• using an inappropriate scale;
• using a graph type that does not suit the data;
• making small differences appear much larger than they really are.

A good statistical graph should present the data clearly, accurately and fairly.

 Summary