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S1 · Bar, Circle, Line and Histogram Graphs

Learn to create and interpret bar, histogram, line, and circle graphs through clear examples and targeted practice.

Alberta Grade 11 Mathematics

Statistics

Alberta Mathematics 20-3 • Study guide S1

Graphs turn data into a picture that is easier to read. A workplace team might compare how many items were packed on different shifts. A weather record might show how temperature changed over several days. The graph type matters: it should match the kind of data and the question. In this lesson, you will practise creating and reading bar graphs, histograms, line graphs, and circle graphs. All example data are hypothetical and are used only for practice.

What you will learn

  • Choose a suitable bar, histogram, line, or circle graph for a set of data.
  • Create a graph with a clear title, labels, scale, and accurate data display.
  • Interpret a graph by comparing values and describing what the data show.

Start with the data and the purpose

Data are facts or measurements collected for a question. A category is a named group, such as a work shift or type of item. A numerical value is a count or measurement linked to a category or time. Before drawing a graph, ask what the data describe and what you want a reader to notice.
A bar graph compares separate categories. Its bars have spaces between them because the categories are distinct. A histogram shows how numerical measurements are spread across intervals, also called bins. The bars touch because the intervals sit next to one another on a number scale. A line graph shows how a value changes across an ordered sequence, often time. A circle graph shows how a whole is divided among categories.
  • Use a bar graph for separate categories.
  • Use a histogram for numerical data grouped into adjacent intervals.
  • Use a line graph when order matters and change across that order is useful to see.
  • Use a circle graph when categories make up one whole.

Make a graph that can be read correctly

Every graph needs a title that tells the reader what is shown. Label each axis, the lines that mark the graph’s horizontal and vertical directions. Include units when values are measurements, such as minutes or kilograms. Choose a scale, the number pattern used along an axis, that fits the data and is easy to follow.
For a bar graph, put the category names along one axis and a numerical scale along the other. Start the value scale at zero so the bar lengths show the values fairly. Leave equal spaces between the bars. For a histogram, mark the numerical intervals along the horizontal axis. Place adjoining bars over the intervals, with no gaps. Each bar’s height represents the number of measurements in that interval.
For a line graph, put the ordered values, such as days, along the horizontal axis. Plot each recorded value and connect the points in order. Do not connect values in an order that changes the meaning of the data. For a circle graph, each category is a part of the full data set. First find the total. Then find each category’s share of that total. The shares must add to the whole. A percentage means a number of parts out of one hundred. If using percents, the category percents should total 100%.
Read the title, labels, and scale before drawing conclusions. A difference of one grid interval may represent one item, five items, or another amount. Check the scale rather than guessing from the picture.
category share=category valuetotal\text{category share} = \frac{\text{category value}}{\text{total}}
  • Give each graph a useful title and labelled axes or categories.
  • Use equal scale steps and show units where needed.
  • Keep the bars separated for categories and touching for histogram intervals.
  • Check that circle-graph categories account for the full data set.

Interpret with care

To interpret a graph, describe what its values show. You can identify the greatest or least value, compare two values, or describe a change across an ordered sequence. Use the graph’s labels and units in your answer. For example, say that a recorded count rose from 12 items to 18 items, rather than saying only that it went up.
A graph shows the data that were collected. It does not, by itself, explain why a value changed. Avoid claiming a cause unless the data provide that information. Also check whether the display could mislead. A cut-off vertical scale on a bar graph can make a small difference look large. A missing category in a circle graph can make the parts fail to represent the whole.
  • Quote values with their units or category names.
  • Describe a pattern without claiming an unsupported cause.
  • Use the scale to judge how large a difference is.

A quick choice guide

Imagine a packing team records output by shift, package weights, total output each day, or how the day’s output is divided among product types. These are different questions, so they call for different graph types. Shift names are separate categories, so a bar graph fits. Package weights can be grouped into adjacent numerical intervals, so a histogram fits. Daily output follows time order, so a line graph fits. Product types that divide a day’s total can be shown with a circle graph.
Before you draw, check that the graph type matches the data. Then organize the values, choose a readable scale, and label the display. Once it is drawn, check that each bar, point, or circle section represents the correct value.
  • The question and data type guide the graph choice.
  • A clear graph makes its information easy to check and interpret.

Worked example

Compare separate categories with a bar graph

A practice packing team records hypothetical numbers of boxes completed by three shifts: morning, 24; afternoon, 18; evening, 30. Create a suitable graph and state which shift completed the most boxes and how many more than the afternoon shift.
Boxes completed by shift
24 boxes18 boxes30 boxesMorningAfternoonEvening

Hypothetical practice counts. Separate categories are shown as bars.

  1. Choose the graph
    The shift names are separate categories, not adjacent numerical intervals. A bar graph is suitable. The values are hypothetical practice data, not actual workplace records.
  2. Set up the display
    Use shift names for the categories and boxes completed for the value scale. A scale from 0 to 30, marked in steps of 5, includes every value and is easy to read. Leave equal gaps between the bars.
    0,5,10,15,20,25,300, 5, 10, 15, 20, 25, 30
  3. Compare values
    The evening shift has the tallest bar at 30 boxes. The afternoon value is 18 boxes. Subtract the smaller count from the larger count to find the difference.
    30−18=1230-18=12
Answer: The evening shift completed the most, with 30 boxes. It completed 12 more boxes than the afternoon shift.
Check: The difference is reasonable because 30 is 12 greater than 18. The scale includes all three values and begins at zero.

Worked example

Group measurements in a histogram

A training exercise records hypothetical package weights, in kilograms. The counts in adjacent intervals are 4 packages from 0 to less than 1 kg, 7 from 1 to less than 2 kg, and 5 from 2 to less than 3 kg. Choose and describe a graph. Which interval has the greatest count?
Package-weight intervals
4 packages7 packages5 packages0 to <11 to <22 to <3

Hypothetical training data grouped in adjacent weight intervals; bar heights show package counts.

  1. Identify the data
    Weight is numerical measurement data. The values are grouped into neighbouring intervals, so a histogram is suitable. The intervals meet without gaps on the number line.
  2. Label the histogram
    Label the horizontal axis package weight in kilograms and the vertical axis number of packages. Draw adjoining bars over the three intervals. Their heights are 4, 7, and 5 packages.
  3. Interpret the bars
    The tallest bar represents the interval from 1 to less than 2 kilograms. Its count is 7 packages, more than the counts in either other interval.
    7>5>47>5>4
Answer: Use a histogram with adjoining bars. The 1 to less than 2 kg interval has the greatest count, at 7 packages.
Check: The three interval counts total 16 packages. The bars should touch because the intervals are adjacent parts of a numerical scale.

Worked example

Show change and parts of a whole

A hypothetical practice log gives daily output of 12, 15, and 18 boxes on Monday, Tuesday, and Wednesday. Another practice record divides 20 boxes into 10 small, 6 medium, and 4 large boxes. Choose a graph for each record. Interpret one useful feature of each.
Box-size shares
Small: 50%Medium: 30%Large: 20%

Hypothetical practice record. The three categories account for all 20 boxes.

  1. Represent change over time
    The weekdays are in order, and the question is about how output changed. A line graph fits. Plot Monday at 12, Tuesday at 15, and Wednesday at 18, then connect the points in that order. The values rise by 3 boxes each day.
    15−12=3,18−15=315-12=3, 18-15=3
  2. Represent the whole
    The three box sizes account for all 20 boxes, so a circle graph can show their shares. Divide each category count by the total to find its fraction. The counts add to 20, so the categories cover the whole record.
    10+6+4=2010+6+4=20
  3. Find the shares
    The small boxes are half of the total, the medium boxes are three tenths, and the large boxes are one fifth. These shares add to one whole. If drawing the circle graph, label each section with its category and share.
    1020=12,620=310,420=15\frac{10}{20}=\frac{1}{2}, \frac{6}{20}=\frac{3}{10}, \frac{4}{20}=\frac{1}{5}
Answer: Use a line graph for daily output; it rises from 12 to 18 boxes. Use a circle graph for the box-size record; small boxes make up half of the 20-box total.
Check: The line graph follows the weekday order. The circle-graph counts total 20, and the three shares total one whole.

Common mistakes and how to avoid them

Leaving gaps between histogram bars.
Correction: Histogram intervals are adjacent, so their bars touch. Use gaps for a bar graph of separate categories.
Choosing a line graph for unordered categories.
Correction: Use a line graph when the order, often time order, matters. Use bars to compare separate category names.
Reading a value without checking the scale.
Correction: Read the axis labels and step size before comparing bar heights or plotted points.
Making circle-graph parts that do not represent the full set.
Correction: Check that the category values add to the total and their shares account for the whole.
Saying a graph proves why a value changed.
Correction: Describe the visible pattern. Do not claim a cause that the data do not establish.

Lesson summary

  • Bar graphs compare separate categories; keep spaces between bars.
  • Histograms show numerical data in adjacent intervals; bars touch.
  • Line graphs show change across an ordered sequence.
  • Circle graphs show how a whole is divided among categories.
  • Titles, labels, units, and readable scales help readers interpret a graph accurately.

Check your understanding

Question 1

A log records the number of service calls on each of five days in order. Which graph best shows whether the number changed over the week?
  1. Bar graph
  2. Histogram
  3. Line graph
  4. Circle graph
Show answer and explanation
Line graph
The days are ordered, and the goal is to show change across that order, so a line graph is suitable.

Question 2

A set of 24 practice items has 12 red, 8 blue, and 4 green items. What fraction of the set is blue?
  1. 1/6
  2. 1/3
  3. 1/2
  4. 2/3
Show answer and explanation
1/3
Blue items are 8 out of 24. The fraction simplifies to 1/3. All category counts add to 24.

Question 3

A histogram uses intervals from 10 to less than 20, 20 to less than 30, and 30 to less than 40 minutes. How should the bars appear?
  1. With equal gaps between them
  2. Touching one another
  3. In a circle
  4. Connected by a line through their tops
Show answer and explanation
Touching one another
These are adjoining numerical intervals, so a histogram uses touching bars.

Key terms

Category
A named group used to organize data, such as a shift or item type.
Interval (bin)
A range of numerical values used to group measurements.
Scale
The number pattern and step size shown on a graph axis.
Percentage
A share expressed as a number of parts out of one hundred.
Histogram
A graph with touching bars that show counts in adjacent numerical intervals.

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برای مبحث S1 · نمودارهای ستونی، هیستوگرام، خطی و دایره‌ای را بسازید و تفسیر کنید در درس Math 20-3، سؤال و تلاش خود را همراه بیاورید. در جلسه می‌توانید محورها را برچسب بزنید و هر ویژگی نمودار را به معادله یا موقعیت مسئله ربط دهید. راهنمای معلم ریاضی را ببینید یا جلسهٔ معارفهٔ رایگان ۳۰ دقیقه‌ای درخواست کنید. زمان جلسه پس از پذیرش معلم قطعی می‌شود.

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Published by DoAssignment. This reviewed lesson follows Alberta Grade 11 Mathematics (Math 20-3), expectation S1. 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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