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D1.1 · Examine the collection, storage, representation, and use of data

Learn to examine the collection, storage, representation, and use of data through clear examples and targeted practice.

Ontario Grade 9 Mathematics

Data

Ontario MTH1W — Strand D: Data Literacy, Expectation D1.1

Every day, data shapes the decisions around you. Schools use attendance data to plan staffing. Streaming services use viewing data to recommend shows. Health agencies use survey data to guide public health policy. But what exactly is data, and how does it travel from a raw observation all the way to a chart on your screen? This lesson traces that full journey — from collection through storage and representation to use — so you can both read data critically and handle it responsibly. No prior statistics knowledge is assumed beyond reading graphs and computing percentages, both of which are reviewed where they appear.

What you will learn

Explain what data is and describe different ways data can be collected.
Identify how data can be stored and organized for later use.
Read and interpret at least two common types of data representations.
Critically evaluate how data is used to support a claim or decision, and identify when a representation might be misleading.

What Is Data and How Is It Collected?

Data are pieces of information recorded about people, objects, or events. A single recorded piece of information is called a data point. A set of many data points collected about the same topic is called a dataset.

Data can be sorted into two broad types. Categorical data places each observation into a named group — for example, a student's favourite sport (soccer, basketball, or swimming). Numerical data records a measured or counted quantity — for example, the number of minutes a student spends on homework each night.

Data is gathered through a process called data collection. Four common methods are used in everyday and research settings. A survey or questionnaire asks people to answer written or online questions. An interview asks questions face-to-face or by phone. Observation records what actually happens without asking anyone — for example, counting cars at an intersection. An experiment deliberately changes one thing and records what happens — for example, testing whether a new study-skills workshop raises quiz scores.

Two key ideas govern collection quality. A population is every person or thing you want information about. A sample is the smaller group you actually measure when the population is too large to reach everyone. For a sample to be trustworthy, it must represent the population fairly — meaning every member of the population has a reasonable chance of being chosen. A sample that leaves out part of the population is called biased, and its data may lead to wrong conclusions.

Data are recorded observations; each single record is a data point.
Categorical data names groups; numerical data measures or counts quantities.
Common collection methods: survey, interview, observation, experiment.
Population = everyone of interest; sample = the group actually measured.
A biased sample does not fairly represent the population.

Storing and Organizing Data

Once data is collected, it must be stored so it can be found, checked, and used later. Raw data — the original, unprocessed records — is often messy. Organizing it carefully is what makes it useful.

The most common way to organize raw data is a data table. A data table arranges information into rows and columns. Each row holds the data for one observation (one person, one trial, or one event). Each column holds all values for one variable. A variable is any characteristic that can differ from one observation to the next — for example, age, favourite colour, or test score.

Today, data is usually stored digitally in a spreadsheet or database. A spreadsheet is a grid of cells arranged in rows and columns — you have likely seen one in a program like Google Sheets. A database is a larger organized system that can store millions of records and allow fast searching. Both formats let users sort, filter, and retrieve specific information without re-reading everything.

Privacy and ethics matter in storage. When data includes personal details — names, ages, addresses — those details must be protected. In Canada, laws set rules about who can collect, store, and share personal data. As a data user, you should always ask: Who collected this? Where is it stored? Who can see it? These questions help you judge whether a dataset was handled responsibly.

Raw data must be organized before it can be used effectively.
A data table uses rows for observations and columns for variables.
Spreadsheets and databases are the main digital storage tools.
A variable is a characteristic that can differ across observations.
Responsible storage protects people's privacy and personal information.

Representing Data: Choosing the Right Display

A data representation is a visual or graphic display that makes patterns in a dataset easier to see. Choosing the right type of display depends on the kind of data you have and the message you want to communicate.

A bar graph uses rectangular bars to show how often each category occurs, or to compare a quantity across categories. The height (or length) of each bar shows the value for that category. Bar graphs work best for categorical data. For example, a bar graph could show how many students in a class chose each type of after-school activity.

A histogram looks similar to a bar graph, but it is used for numerical data grouped into ranges called intervals or bins. Unlike a bar graph, the bars in a histogram touch each other because the data is continuous — there are no gaps between intervals. For example, you could display homework times grouped as 0–19 minutes, 20–39 minutes, and 40–59 minutes.

A circle graph (also called a pie chart) shows how a whole dataset is divided into parts. Each slice represents a category, and the size of each slice shows that category's share of the total, usually written as a percent. Circle graphs are most useful when you want to show how parts relate to a whole. A line graph connects data points with a line and is best for showing how a numerical value changes over time.

Every graph must include a title (what the graph is about), labelled axes or sections, and a scale or units so the reader knows what the numbers mean. A graph without these features is incomplete and can be misleading.

Percent for one category =

\frac{frequency of category}{total number of data points}

× 100

Choose the display type based on whether data is categorical or numerical.
Bar graph: compares categories. Histogram: shows distribution of numerical data in intervals.
Circle graph: shows parts of a whole as percents. Line graph: shows change over time.
Every graph needs a title, labelled axes or sections, and clear units.
Missing labels or a broken scale can make a graph misleading.

Using Data: Making Sense of What It Shows

Collecting, storing, and displaying data are all steps toward the real goal: using data to answer a question or support a decision. This section looks at how to read a data display carefully and how to spot when data is being used unfairly.

When you look at a data display, start by reading the title and all labels before drawing any conclusion. Ask: What question was this data collected to answer? Who collected it, and how? How large is the sample? A result from a sample of 10 people is much less reliable than the same result from a sample of 500 people, even if the graph looks the same.

Data can be used to identify a trend (a general direction of change over time), to compare groups, or to support an argument. However, data can also be presented in ways that exaggerate or hide the truth. A common trick is a broken or compressed axis — when the vertical axis of a bar graph does not start at zero, even a small difference between bars looks huge. Another issue is cherry-picking: showing only the data points that support one side of an argument and ignoring the rest.

A responsible reader always checks: Does the scale start at zero, or is it cut off? Are all categories shown, or are some missing? Is the sample size large enough and representative? Does the conclusion stated in the headline actually match what the data shows? Asking these questions turns you from a passive viewer into a critical reader of data.

Always read the title, labels, and scale before interpreting a graph.
A larger, representative sample produces more reliable conclusions.
A compressed or broken axis can make small differences look large.
Cherry-picking shows only favourable data points and hides others.
Check that any conclusion drawn is actually supported by the data shown.

Choosing the Right Data Display

Display Type	Best Used For	Data Type	Key Feature
Bar graph	Comparing amounts across categories	Categorical	Bars do not touch; gaps between bars
Histogram	Showing how data spreads across intervals	Numerical (grouped)	Bars touch; no gaps between intervals
Circle graph	Showing each part as a percent of the whole	Categorical	Slices must add up to 100%
Line graph	Showing how a value changes over time	Numerical (over time)	Points connected by a line to show trend

Worked example

Reading and Evaluating a Data Display

A school surveyed 200 students and asked: 'What is your main after-school activity?' The results were: Homework — 70 students, Sports — 60 students, Video games — 50 students, Reading — 20 students. A student creates a circle graph to display these results. (a) Calculate the percent of students who chose each category. (b) Identify which category should have the largest slice. (c) The graph's title says 'Most students prefer homework.' Is this conclusion fully supported by the data? Explain.

Step 1 — Recall the percent formula
To find the percent for each category, divide the number of students in that category by the total number of students surveyed, then multiply by 100. The total here is 200 students.
$\text{Percent} = \frac{\text{frequency}}{\text{total}} \times 100$
Step 2 — Calculate percent for Homework
70 students chose Homework out of 200 total.
$\frac{70}{200} \times 100 = 35\%$
Step 3 — Calculate percent for Sports
60 students chose Sports out of 200 total.
$\frac{60}{200} \times 100 = 30\%$
Step 4 — Calculate percent for Video games
50 students chose Video games out of 200 total.
$\frac{50}{200} \times 100 = 25\%$
Step 5 — Calculate percent for Reading
20 students chose Reading out of 200 total.
$\frac{20}{200} \times 100 = 10\%$
Step 6 — Verify the percents add to 100%
Add all four percents to confirm they account for the entire dataset.
$35 + 30 + 25 + 10 = 100\%$
Step 7 — Identify the largest slice
Homework has the highest percent at 35%, so it gets the largest slice in the circle graph.
$\text{Largest slice} = 35\% \text{ (Homework)}$
Step 8 — Evaluate the conclusion
The title claims 'Most students prefer homework.' The word 'most' usually means more than half, which would be more than 50%. Homework was chosen by only 35% of students — the largest single share, but not a majority. The correct statement is that homework was the most popular single choice, not that most students prefer it. The title overstates what the data shows.
$35% < 50%$

Answer: (a) Homework 35%, Sports 30%, Video games 25%, Reading 10%. (b) Homework should have the largest slice. (c) No — 35% is the largest single category but is not a majority. The title overstates the conclusion.

Check: Verify: 70 + 60 + 50 + 20 = 200 students total. Each percent was calculated by dividing by 200 and multiplying by 100. All percents sum to 100%. The critical evaluation in Step 8 is confirmed because 35% is clearly less than 50%.

Common mistakes and how to avoid them

Using a circle graph when the percents do not add up to 100%. This happens when a survey allows multiple answers per person.

Correction: A circle graph only works when each person or observation belongs to exactly one category so that all slices together make up the whole dataset (100%).

Treating a sample conclusion as if it applies perfectly to the entire population, without checking sample size or representativeness.

Correction: Always ask how large the sample is and whether it was chosen fairly. A small or biased sample may not reflect the population accurately.

Confusing a bar graph with a histogram and leaving gaps between bars in a histogram.

Correction: Histograms display numerical data in touching intervals — the bars must touch because there are no gaps between the number ranges.

Reading a graph without checking the scale, and missing that the vertical axis starts at a value other than zero.

Correction: Always examine the axis scale first. A y-axis that starts above zero makes differences between bars look much larger than they really are.

Mixing up categorical and numerical data when choosing a display, such as drawing a histogram for favourite colours.

Correction: Histograms are for numerical data grouped into intervals. Use a bar graph for categorical data like names of colours, sports, or activities.

Lesson summary

Data are recorded observations. Each individual record is a data point, and a collection of records is a dataset.
Data can be categorical (named groups) or numerical (measured or counted values).
Common collection methods include surveys, interviews, observation, and experiments. A sample must fairly represent the population to produce trustworthy data.
Organized data is stored in tables, spreadsheets, or databases. Each row is one observation; each column is one variable. Protecting personal data is an ethical responsibility.
The right display type depends on the data: bar graphs for comparing categories, histograms for numerical intervals, circle graphs for parts of a whole, and line graphs for change over time.
Critical reading of data means checking the title, labels, scale, sample size, and whether the stated conclusion is actually supported by what the data shows.

Check your understanding

Question 1

A researcher records the favourite music genre of every student in a school. What type of data is this?

Numerical data, because students are counted.
Categorical data, because genres are named groups.
Experimental data, because a school was involved.
Continuous data, because music plays over time.

Show answer and explanation

Categorical data, because genres are named groups.

Favourite music genre places each student into a named group (pop, hip-hop, classical, etc.). Named groups are the defining feature of categorical data. Counting how many students chose each genre produces numbers, but the variable itself — genre — is categorical.

Question 2

A bar graph comparing four after-school clubs shows the vertical axis running from 40 to 60 members. Club A has 58 members and Club B has 42 members. On this graph, Club A's bar looks about four times as tall as Club B's bar. Which statement best describes this graph?

The graph is accurate because the data values are correct.
The graph is misleading because the axis does not start at zero, making the difference look larger than it is.
The graph is misleading because a histogram should have been used instead.
The graph is accurate because circle graphs cannot show this data.

Show answer and explanation

The graph is misleading because the axis does not start at zero, making the difference look larger than it is.

The actual difference is 58 − 42 = 16 members, which is small relative to the totals. Because the axis starts at 40 instead of 0, that small gap is stretched across the whole height of the graph, making Club A look far larger than Club B. This is a classic misleading scale.

Question 3

A school wants to find out whether Grade 9 students support a new lunch-hour policy. Which sample would be the most representative of all Grade 9 students in the school?

Asking only the students in the student council.
Asking only students who eat in the cafeteria every day.
Randomly selecting 60 students from the complete list of all Grade 9 students.
Asking the 10 students who arrive earliest each morning.

Show answer and explanation

Randomly selecting 60 students from the complete list of all Grade 9 students.

A random selection from the complete list gives every Grade 9 student an equal chance of being chosen. The other options each favour a specific sub-group (council members, regular cafeteria users, early arrivers) and would likely produce biased results.

Question 4

A dataset records the daily high temperature (in °C) in Toronto for every day of January. Which display is most appropriate for showing how the temperature changed day by day throughout the month?

A circle graph, because temperature data must always show parts of a whole.
A bar graph, because temperature is a category.
A line graph, because it shows how a numerical value changes over time.
A histogram, because the temperatures can be grouped into intervals.

Show answer and explanation

A line graph, because it shows how a numerical value changes over time.

A line graph connects numerical data points in time order and clearly shows the trend — rises, falls, and fluctuations — across the month. A histogram could group temperatures but would lose the day-by-day pattern. A circle graph is for parts of a whole, not for change over time.

Key terms

Data: Recorded pieces of information about people, objects, or events.
Data point: One single recorded observation within a dataset.
Categorical data: Data that places each observation into a named group or category (e.g., favourite colour).
Numerical data: Data that records a measured or counted quantity (e.g., height in centimetres).
Population: Every person or thing you want information about in a study.
Sample: The smaller group selected from the population that is actually measured or surveyed.
Biased sample: A sample that does not fairly represent the population because some members were much more or less likely to be chosen.
Variable: Any characteristic that can differ from one observation to the next in a dataset.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 9 Mathematics (MTH1W), expectation D1.1. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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