1. Qualitative vs quantitative data

1. Qualitative vs quantitative data

Qualitative data = qualities

Information that describes the characteristics or qualities of something. It is usually descriptive rather than numerical.

Examples:

• An apple is red.

• A rock is rough.

• A liquid smells sweet.

• A bird has black feathers.

Memory trick: Qualitative = qualities.

Quantitative data = quantities

Information expressed as numbers that you can count or measure.

Examples:

• The plant is 15 cm tall.

• The temperature is 24°C.

• There are 12 students.

• The rock has a mass of 300 g.

Memory trick: Quantitative = quantities and numbers.

How to tell them apart

Ask yourself: Is it describing what something is like, or giving a number?

A little trick: numbers don't always automatically mean quantitative measurements in every context. But for your school science test, counting and measuring are the main things to recognise as quantitative data.

2. First-hand vs second-hand data

First-hand data (primary data)

Data you collect yourself, directly from an investigation, experiment, observation or survey.

Examples:

• Measuring how tall plants grow.

• Counting birds in your backyard.

• Asking 20 students about their favourite subject.

• Recording the temperature each day.

Second-hand data (secondary data)

Data that someone else has already collected, which you use for your own work.

Examples:

• Getting rainfall measurements from a government website.

• Using results from a published scientific study.

• Reading statistics in a textbook.

• Using a graph made by another researcher.

Important: It's about who collected the data, not whether you see it online or on paper.

For example, if you conduct your own online survey, that's first-hand data. If you look up somebody else's survey results online, that's second-hand data.

3. Scientific models

A scientific model is a simplified representation of something in the real world that helps us understand, explain or predict how it works.

Examples of scientific models include:

• A model of the solar system.

• A diagram of a plant or animal cell.

• A model of an atom.

• A diagram of the water cycle.

• A computer simulation of a cyclone.

Why do scientists use models?

• To explain things that are too small to see, like atoms.

• To represent things that are too large to study all at once, like Earth.

• To show processes that are difficult to observe directly.

• To make predictions and test ideas.

What are the limitations of models?

A model is not exactly the same as reality. It leaves out some details or simplifies things.

For example, a classroom solar system model might show planets much closer together than they really are, and the planets may not be drawn to scale.

A common test question is: Why are scientific models useful but limited?

A good answer: They help us understand and predict how things work, but they simplify reality and may leave out important details.

4. Range, mean, median and mode

These four words are extremely important because they help you understand a set of numbers. Let's use the same example for all four.

Imagine five students recorded how many hours they spent studying:

2, 4, 4, 6, 9

Range

The difference between the biggest and smallest numbers.

\[ \text{Range}=\text{Highest}-\text{Lowest} \]

\(9-2=\boxed{7}\)

Memory trick: Range = the distance between the ends.

Mean

The average. Add all the numbers and divide by how many numbers there are.

\[ \text{Mean}=\frac{\text{Sum of values}}{\text{Number of values}} \]

\[ \frac{2+4+4+6+9}{5}=\boxed{5} \]

Memory trick: Mean = add, then divide.

Median

The middle number when the data is arranged in order.

2, 4, 4, 6, 9

Median = \(\boxed{4}\)

Memory trick: Median = middle.

Mode

The number that occurs most often.

2, 4, 4, 6, 9

Mode = \(\boxed{4}\)

Memory trick: Mode = most common.

What if there are two middle numbers?

For example: 2, 3, 7, 9.

There are four numbers, so the middle two are 3 and 7. Add them and divide by 2:

\[ \text{Median}=\frac{3+7}{2}=\boxed{5} \]

The median is 5, even though 5 isn't in the original list.

What if numbers repeat?

• A data set can have no mode if every number occurs equally often.

• It can have two modes if two numbers tie for occurring most often.

• Always put the numbers in order before finding the median.

Your turn — try these

Here are the numbers: 3, 5, 5, 7, 10

1. What is the range?

Highest minus lowest.

2. What is the mean?

Add the numbers, then divide by 5.

3. What is the median?

Find the middle number.

4. What is the mode?

Find the most common number.

Check answersTry again

5. Variables

A variable is something that can change during an experiment.

There are three main types you should learn.

Independent variable

The thing you deliberately change.

Example: You give plants different amounts of sunlight.

Independent = what I change.

Dependent variable

The thing you measure to see what happened.

Example: You measure how tall the plants grow.

Dependent = what I measure.

Controlled variables

The things you keep the same to make the experiment fair.

Example: Use the same type of plant, same soil and same amount of water.

Controlled = what I keep the same.

Example test question

A student investigates whether the amount of sunlight affects plant growth.

• Independent variable: amount of sunlight.

• Dependent variable: plant growth or height.

• Controlled variables: type of plant, soil, water and pot size.

Why do we control variables?

To make it a fair test, so the results are more likely to show the effect of the independent variable.

A helpful sentence starter for tests is:

"The independent variable is ___ because it is the factor being deliberately changed."

6. Graphing

Graphs help scientists present data so that patterns and relationships are easier to understand.

Line graph

Best for showing changes over time or continuous data.

Example: Plant height over 10 days, or temperature throughout a week.

Bar graph

Best for comparing separate categories.

Example: Number of students who prefer apples, bananas or oranges.

Scatter plot

Best for investigating the relationship between two numerical variables.

Example: Whether more sunlight is associated with taller plants.

Parts of a good graph

1. Title: explains what the graph shows.

2. X-axis (horizontal): usually shows the independent variable.

3. Y-axis (vertical): usually shows the dependent variable.

4. Axis labels: identify what is being measured and its units, if applicable.

5. Scale: evenly spaced intervals that fit the data.

6. Data points or bars: accurately represent the results.

For example, if you are measuring plant height over time:

• Title: Effect of Time on Plant Growth

• X-axis: Time (days)

• Y-axis: Plant height (cm)

Common test question: Which graph would you use to show how temperature changes over seven days?

Answer: A line graph, because it shows changes over time.

Remember: bar graphs usually have gaps between their bars because the categories are separate. Line graphs connect points when showing a continuous trend or change over time.

Your Data Science cheat sheet

This is the shorter version I'd recommend putting on your revision sheet. You can copy it into your notes and shorten it further if your teacher has limited the size.

DATA SCIENCE — CHEAT SHEET

1. Types of data

• Qualitative = descriptions/qualities (e.g. colour, texture, smell).

• Quantitative = numbers, counts or measurements (e.g. 15 cm, 20 students).

2. Collecting data

• First-hand/primary = collected by you.

• Second-hand/secondary = collected by someone else and reused.

3. Scientific models

• A simplified representation of a real object, system or process.

• Uses: explain, understand and predict.

• Limitations: may leave out details or not be to scale.

4. Statistics

• Range = highest − lowest.

• Mean = total ÷ number of values.

• Median = middle value after ordering.

• Mode = most frequent value.

• For an even number of values, median = average of the two middle values.

5. Variables

• Independent = deliberately changed.

• Dependent = measured/observed.

• Controlled = kept the same for a fair test.

6. Graphs

• Line graph = changes over time/continuous data.

• Bar graph = compares categories.

• Scatter plot = relationship between two numerical variables.

• X-axis = horizontal; usually independent variable.

• Y-axis = vertical; usually dependent variable.

• Include a title, labelled axes, units, suitable scale and accurate data.

• Fair test = change one independent variable and control other relevant factors.

General science knowledge you should also know

These aren't separate topics on the little sheet, but they are useful foundations for answering science questions.

Let's test what you've learned