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D1.5 · Classify one-variable data and choose suitable displays

Learn to classify one-variable data and choose suitable displays through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Data Management

Ontario Grade 11 MBF3C — Study topic D1.5

A school club is deciding what snacks to order. It might record each student’s favourite snack, the number of siblings each student has, or each student’s height. These are all data about one variable at a time, but they are not the same kind of data. The type of data helps determine a useful display. This lesson focuses on classifying one-variable data and choosing displays that fit.

What you will learn

1. Begin with the variable

A variable is the feature or value being recorded for each person or item. For example, if a survey asks each student for a favourite snack, the variable is favourite snack. If it records the number of siblings, the variable is number of siblings.
One-variable data means that the data set records one feature for each case. A case is one person or item being described. A list of students’ heights is one-variable data. Recording each student’s height and favourite snack together involves two variables, not one.
Before choosing a display, ask: What is being recorded? What kinds of values can it have? A display is suitable when it represents those values clearly and helps answer the question being asked.

2. Classify the data

Categorical data place cases into groups or labels. Examples include favourite snack, type of transport, and school team. The values name categories rather than amounts. A category can be written as a word or label, even if a code is used to represent it.
Numerical data are values that represent counts or measurements. The number of siblings is a count. Height is a measurement. Numerical data can be discrete or continuous.
Discrete data come from counting separate items. The values are countable and usually whole numbers, such as the number of pets in a household. A value such as 2.5 pets would not make sense in this context.
Continuous data come from measuring. A measurement can take values within a range, including decimal values, depending on the measuring tool. For example, a person’s height might be recorded as 168 cm or 168.4 cm. The actual height is measured, even if it is rounded when written down.
The wording of a question matters. “How many minutes did you read?” is a measurement of time and can be continuous, even if a person reports a whole number of minutes. “How many books did you read?” is a count and is discrete.

3. Match the display to the data

A bar graph is useful for categorical data. Each bar represents a category, and the bar heights or lengths show how many cases belong to each category. Bars are separated because the categories are distinct. A bar graph is a good choice when comparing category counts.
A circle graph can show how categories make up a whole. It is useful when the goal is to compare each category’s share of the total. The categories should account for the whole data set, and the graph should make the parts clear.
A dot plot is useful for a small set of numerical values, especially when values repeat. Each dot stands for one case. Stacks of dots make common values and the spread of the data easy to notice.
A histogram is useful for numerical data when many values cover a range. The values are grouped into intervals, and touching bars show how many observations fall in each interval. It gives a picture of where values cluster and how they are spread out.
A stem-and-leaf plot organizes numerical values while keeping the original values visible. It can be useful for a modest-sized set of whole-number data. A stem groups leading digits, and a leaf records the remaining digit. A key explains how to read the entries, such as 16∣4=16416\mid 4=164. For measured values, the key must make the place value clear.

4. Make the choice for a reason

A display is not chosen just because it looks familiar. First classify the variable. Then consider the size and purpose of the data set. A small list of numerical values may be easiest to read in a dot plot. A larger set of measurements may be clearer in a histogram because intervals summarize the values.
Also consider the question. If the question asks which category is most common, a bar graph makes category counts easy to compare. If it asks how numerical measurements are distributed, a histogram or dot plot may be more helpful.
Labels and scales matter. Include a clear title, label the variable, and show what the counts or intervals mean. A display with unclear labels can lead readers to misunderstand the data, even when the chosen display type is appropriate.

Worked example

Example 1: Favourite ways to get to school

A class survey records one response from each of 24 students about their usual way of getting to school: walk, bus, car, or bicycle. Classify the variable and choose a suitable display for comparing the responses.
  1. Name the variable
    The variable is each student’s usual way of getting to school. Each response is a label, not a count or measurement.
  2. Classify the data
    Walk, bus, car, and bicycle are categories. The data are categorical because the values sort students into groups.
  3. Choose a display
    A bar graph is suitable because the goal is to compare how many students chose each category. Separate bars make the categories distinct and allow their counts to be compared.
Answer: The variable is categorical. Use a bar graph to compare the number of students in each travel category.
Check: The responses are labels, so a numerical display such as a histogram would not suit this variable.

Worked example

Example 2: Time spent reading

A group records the reading time, in minutes, for 18 students during one evening. The times range from 12 to 58 minutes and include values recorded to the nearest minute. Classify the variable and choose a display to show how the times are spread out.
  1. Name the variable
    The variable is the time each student spent reading. It is a measurement of time, even though the recorded values are rounded to whole minutes.
  2. Classify the data
    Time is numerical and can vary across a range. It is continuous data; recording to the nearest minute does not turn the measured quantity into a count.
  3. Choose a display
    A histogram is suitable for showing how these numerical measurements are spread across a range. Grouping the times into intervals helps summarize a set of 18 observations.
Answer: The variable is continuous numerical data. Use a histogram to show the distribution of reading times across intervals.
Check: The values describe measured time, not a number of separate items. A bar graph of categories would not match the variable.

Common mistakes and how to avoid them

Calling any data written with numbers numerical data.
Correction: Check what the values mean. A number used only as a label, such as a jersey number, is categorical; a count or measurement is numerical.
Calling measured data discrete because the recorded values are whole numbers.
Correction: Classify the quantity, not just the written format. A measurement such as time or height is continuous even when rounded.
Using a histogram for categories.
Correction: Histograms group numerical values into intervals. Use a bar graph to compare distinct categories.
Choosing a display without considering the question.
Correction: Decide what the reader needs to compare or understand, then choose a display that makes that feature clear.

Lesson summary

Check your understanding

Question 1

A survey records the number of pets owned by each student. Which classification and display are most suitable for a small class data set?
  1. Categorical data; bar graph
  2. Discrete numerical data; dot plot
  3. Continuous numerical data; histogram
  4. Categorical data; circle graph
Show answer and explanation
Discrete numerical data; dot plot
The number of pets is a count, so it is discrete numerical data. For a small set of counts, a dot plot can show repeated values clearly.

Question 2

A coach records each player’s height to the nearest centimetre. Which statement is correct?
  1. It is categorical data because centimetres are labels.
  2. It is discrete data because the recorded heights are whole numbers.
  3. It is continuous numerical data because height is measured.
  4. It is categorical data and should be shown with a circle graph.
Show answer and explanation
It is continuous numerical data because height is measured.
Height is a measurement and is continuous numerical data. Rounding the recorded values to whole centimetres does not change the type of quantity.

Question 3

A group wants to show how a set of many numerical test times is spread across intervals. Which display is a suitable choice?
  1. Histogram
  2. Bar graph of named categories
  3. Circle graph
  4. A list of category labels
Show answer and explanation
Histogram
A histogram groups numerical measurements into intervals and shows how observations are distributed across them.

Key terms

Variable
The feature or value recorded for each person or item.
Case
A person or item described by the data.
Categorical data
Data whose values are group names or labels.
Numerical data
Data whose values represent counts or measurements.
Discrete data
Numerical data from counting separate items.
Continuous data
Numerical data from measuring a quantity that can vary across a range.
Display
A visual way to organize and show data.
Interval
A range of numerical values grouped together in a display.

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About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MBF3C), expectation D1.5. It is a study resource, not an official curriculum publication.

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