Chapter 10 · Measurement and data
Read and Make Bar Graphs
Read each bar's value, even when it ends between two numbers. Compare bars, find totals and differences, and make your own bar graph from a table.
A bar graph uses bars so you can see and compare amounts at a glance. Each bar stands for one category, which is one of the groups being compared, such as a day of the week. The height of a bar shows that category's value, or amount.
Beside the bars is the scale. It is a number line that starts at 0 and goes up in equal steps, so each line on it is the same amount more than the line below. The unit tells what the values measure, such as minutes. The two edges of the graph are its axes. One axis names the categories, and the other holds the scale.
In this lesson you will read bar graphs and then make one of your own. Here the bars stand up from the bottom, so you read the top of each bar. The graph below shows how many minutes Maya read on each school day.
In Maya's graph, each bar stands for the day written under it. The label on that axis, Day, tells you the categories are days. The other axis holds the scale. Its label, Minutes, gives the unit. The scale runs from 0 at the bottom to 60 minutes at the top.
To read a bar, look straight across from its top to the scale. Here are the values the five bars show:
- Monday: 30 minutes
- Tuesday: 55 minutes
- Wednesday: 20 minutes
- Thursday: 40 minutes
- Friday: 45 minutes
Key concept
The scale gives each bar its value
A bar's value is the number on the scale that is level with its top. The scale starts at 0 and goes up in equal steps, so equal spaces on it always stand for equal amounts. That is why you can also read a top that falls between two numbers. Work out what part of the way it is from the number below it to the number above it. When you make a bar graph, you choose the step.
Worked example
A bar that ends between two numbers
Picture a bar graph of points scored. Its scale is numbered 0, 10, 20, 30 and so on, up to 100. Halfway between each pair of numbers is a line with no number. One bar ends on the line between 50 and 60. How many points does that bar show?
Find the numbers just below and just above the top of the bar. They are 50 and 60, so the bar shows more than 50 points and fewer than 60.
Find the gap between those two numbers by subtracting the smaller one from the larger one.
The lines on a scale are equally spaced. The line with no number cuts the gap into 2 equal spaces, so each space is worth half of 10.
The top of the bar is one space above 50, so add the worth of one space to 50.
Answer
The bar shows 55 points, halfway between 50 and 60.
Worked example
Compare, subtract and add
Use Maya's graph above. On which day did she read the most, and on which day the least? How many more minutes did she read on the most day than on the least day? How many minutes did she read in all?
Compare the bars. All five bars use the same scale, so a taller bar means more minutes. Tuesday's bar is the tallest, at 55 minutes. Wednesday's bar is the shortest, at 20 minutes. Putting all five values in order shows the same thing.
“How many more” asks for the difference, the amount by which one value is greater than another. Subtract the least value from the greatest.
“In all” asks for the total, so add all five values. You can add in any order, so pair numbers that make easy sums first.
Answer
Maya read the most on Tuesday and the least on Wednesday; she read 35 more minutes on Tuesday than on Wednesday and 190 minutes in all.
To make a bar graph from a table, you choose the scale. Start it at 0, so each bar's height shows its whole value. Then pick a step, and keep every step the same size, so equal spaces stand for equal amounts. Use enough steps to reach the greatest value in the table, so the tallest bar fits.
The step does not have to fit evenly into every value. A multiple of the step is a number you land on when you count by the step from 0. If a value is not a multiple of the step, its bar ends between two lines. You place its top the same way you read one, by working out what part of the way it is between those lines. You could pick a very small step, such as 1, but then you would need very many steps. That graph is not wrong, but it is hard to read.
Last, label the graph. Name each bar, label the axis under the bars with what the categories are, and label the scale with its unit. You can also give the graph a title.
The table below shows how many pounds of food three classes collected for a food drive.
| Class | Food collected (pounds) |
|---|---|
Class A | 40 |
Class B | 65 |
Class C | 50 |
Worked example
Make a bar graph from a table
Make a bar graph of the food drive table above. Class A collected 40 pounds, Class B collected 65 pounds, and Class C collected 50 pounds.
Find the greatest value, because the scale has to reach it. Class B collected the most, 65 pounds.
Start the scale at 0 and pick a step. Other steps would work, but 10 is quick to count by and needs only a few lines. Six steps of 10 reach only 60, which is less than 65, so the tallest bar would not fit. Seven steps reach 70, which is enough.
Label the graph. Write Class A, Class B and Class C along the bottom, where the bars will go, and label that axis Class, because the categories are classes. Label the scale with the unit, Pounds. Then give the graph a title, such as Food Drive Totals.
Draw each bar up to its value. Class A's bar stops level with 40, and Class C's bar stops level with 50. Counting by 10s jumps from 60 to 70, so 65 is not a multiple of 10. Class B's bar stops between those two lines, halfway, because 65 is 5 more than 60 and 5 is half of 10.
Answer
The graph you make has a scale from 0 to 70 pounds in steps of 10, with labelled bars for Class A at 40 pounds, Class B at 65 pounds (halfway between 60 and 70) and Class C at 50 pounds.
Takeaway: A bar graph's scale starts at 0 and goes up in equal steps, so the top of each bar lines up with one value, whether it is level with a number or between two. Read those values to compare bars and to find differences and totals. To make a bar graph, choose a step, use enough steps to reach the greatest value, and label the bars, the axes and the unit.
Next, you will read and make line graphs, which show how a value changes over time.