Reading, Plotting and Interpreting Bar Graphs for Primary 4

Bar Graph

Performance Objectives

By the end of the lesson, students should be able to:

1. draw bar graph;
2. read bar graph;
3. identify bar graph mode.

Understanding Data

In our daily lives, we often collect information about different things. This information is called data. For example, we might want to know how many pupils like mangoes, oranges, or bananas in a class. Or we might want to know the number of boys and girls in Primary 4.

When we have a lot of data, it can be hard to understand just by looking at numbers. Graphs help us to see and compare this information easily. A bar graph is one way to show data using bars.

What is a Bar Graph?

A bar graph is a chart that uses rectangular bars to show and compare different amounts of data.

The bars can be drawn either vertically (standing up) or horizontally (lying down). The length or height of each bar shows the quantity or amount of the item it represents. Bar graphs make it easy to see which items have more or less and to compare them quickly.

Parts of a Bar Graph

Every bar graph has important parts that help us understand the information it shows. These parts include:

1. Title: This tells us what the graph is about. For example, “Favourite Fruits of Primary 4 Pupils”.

2. Axes: A bar graph has two main lines called axes. One axis is for the categories (like names of fruits or colours), and the other axis is for the numbers (like how many pupils). The horizontal line is called the x-axis, and the vertical line is called the y-axis.

3. Labels: These are words or numbers that tell us what each axis represents. For example, the x-axis might be labelled “Fruits” and the y-axis “Number of Pupils”.

4. Scale: This is the numbering on the axis that shows the quantity. It tells us what each mark or line on the number axis stands for. For example, each line might represent 1 pupil, or 2 pupils, or 5 pupils, depending on the data.

5. Bars: These are the rectangular blocks that show the data. The height or length of each bar tells us the amount for that category.

Types of Bar Graphs

Bar graphs can be drawn in two main ways:

1. Vertical Bar Graph: In this type, the bars stand upright. The categories are usually on the horizontal (x) axis, and the numbers are on the vertical (y) axis.

2. Horizontal Bar Graph: In this type, the bars lie flat. The categories are usually on the vertical (y) axis, and the numbers are on the horizontal (x) axis.

Reading a Bar Graph

Reading a bar graph means understanding the information it presents. To read a bar graph, follow these steps:

1. Read the Title: This tells you what the graph is about.

2. Look at the Axis Labels: See what each axis represents (e.g., “Days of the Week” and “Number of Visitors”).

3. Understand the Scale: Check the numbers on the counting axis to know what each line or mark means (e.g., 1 unit = 1 person, or 1 unit = 5 items).

4. Find the Value for Each Bar: Look at the end of each bar and trace a line to the number axis to find its value. For vertical bars, look at the height. For horizontal bars, look at the length.

5. Compare Information: You can compare the heights or lengths of the bars to see which category has the most, the least, or how much more one has than another.

Worked Example 1: Reading a Bar Graph

Look at the bar graph below, which shows the number of pupils who chose different sports as their favourite.

From the graph, we can read the following information:

1. The title is “Favourite Sports”.
2. The x-axis shows “Sports” (Football, Basketball, Running, Swimming).
3. The y-axis shows “Number of Pupils”.
4. The scale on the y-axis goes up by 2s (0, 2, 4, 6, 8, 10, 12).

5. Number of pupils who like Football: The bar for Football reaches 10. So, 10 pupils like Football.

6. Number of pupils who like Basketball: The bar for Basketball reaches 6. So, 6 pupils like Basketball.

7. Number of pupils who like Running: The bar for Running reaches 8. So, 8 pupils like Running.

8. Number of pupils who like Swimming: The bar for Swimming reaches 4. So, 4 pupils like Swimming.

We can also see that Football is the most popular sport because its bar is the tallest.

Generating Data for a Bar Graph

Before drawing a bar graph, we need to collect data. Generating data means gathering information about a topic. This can be done by asking questions, counting items, or observing things.

For Primary 4, we will generate simple data. For example, we can ask our classmates about their favourite subjects or count the number of different types of trees in the school compound.

Example: Generating Data

A teacher asked Primary 4 pupils about their favourite subjects. Here are their responses:

Mathematics: 7 pupils

English: 9 pupils

Science: 5 pupils

Social Studies: 4 pupils

This collected information is the data we will use to plot a bar graph.

Plotting a Bar Graph

Plotting a bar graph means drawing it using the collected data. Follow these steps to draw a bar graph:

The procedure involves the following steps:

1. Draw the Axes: Draw a horizontal line (x-axis) and a vertical line (y-axis) that meet at a point. Use a ruler to make them straight.

2. Choose a Title: Write a clear title for your graph at the top. This tells everyone what the graph is about.

3. Label the Axes: Decide what each axis will represent. For a vertical bar graph, the categories (e.g., subjects, items) go on the x-axis, and the numbers (e.g., number of pupils, quantity) go on the y-axis. For a horizontal bar graph, it is the other way around.

4. Choose a Scale: Look at your data and decide on a suitable scale for the number axis. The scale should allow all your data to fit on the graph. For example, if your numbers are small (like 1 to 10), you can use a scale of 1 unit = 1 item. If numbers are larger, you might use 1 unit = 2 items or 1 unit = 5 items.

5. Draw the Bars: For each category, draw a rectangular bar. The height (for vertical) or length (for horizontal) of the bar must match the number it represents on your scale. Make sure all bars have the same width and there is an equal space between them.

Worked Example 2: Plotting a Vertical Bar Graph

Plot a vertical bar graph for the favourite subjects data:

Mathematics: 7 pupils

English: 9 pupils

Science: 5 pupils

Social Studies: 4 pupils

Steps:

1. Draw the x-axis and y-axis.

2. Title the graph: “Favourite Subjects of Primary 4 Pupils”.

3. Label the x-axis “Subjects” and the y-axis “Number of Pupils”.

4. Choose a scale for the y-axis. Since the highest number is 9, a scale of 1 unit = 1 pupil is good. Mark numbers from 0 to 10 on the y-axis.

5. Draw the bars:

   1. For Mathematics, draw a bar up to 7 on the y-axis.
   2. For English, draw a bar up to 9 on the y-axis.
   3. For Science, draw a bar up to 5 on the y-axis.
   4. For Social Studies, draw a bar up to 4 on the y-axis.

Worked Example 3: Plotting a Horizontal Bar Graph

A shop sold different numbers of drinks in one hour:

Malt: 8 bottles

Coke: 12 bottles

Fanta: 6 bottles

Sprite: 10 bottles

Steps:

1. Draw the x-axis and y-axis.

2. Title the graph: “Drinks Sold in One Hour”.

3. Label the y-axis “Drinks” and the x-axis “Number of Bottles”.

4. Choose a scale for the x-axis. Since the highest number is 12, a scale of 1 unit = 2 bottles is good. Mark numbers from 0 to 12 (0, 2, 4, 6, 8, 10, 12) on the x-axis.

5. Draw the bars:

   1. For Malt, draw a bar across to 8 on the x-axis.
   2. For Coke, draw a bar across to 12 on the x-axis.
   3. For Fanta, draw a bar across to 6 on the x-axis.
   4. For Sprite, draw a bar across to 10 on the x-axis.

Bar Graph Mode

The mode in a bar graph is the category that has the highest frequency or the largest number.

In simple terms, the mode is the item that appears most often in the data. On a bar graph, the mode is easily identified as the bar that is the tallest (for vertical graphs) or the longest (for horizontal graphs).

Worked Example 4: Identifying Bar Graph Mode

Look at the “Favourite Sports” bar graph again:

To find the mode, we look for the tallest bar. In this graph, the bar for Football is the tallest, reaching 10 pupils. Therefore, the mode is Football.

Worked Example 5: Identifying Bar Graph Mode

Look at the “Drinks Sold in One Hour” bar graph again:

To find the mode, we look for the longest bar. In this graph, the bar for Coke is the longest, reaching 12 bottles. Therefore, the mode is Coke.