Read and Create Bar Graphs | Grade 6 Math | LevelKite

A bar graph shows one value for each category as a bar. A category is one group being compared, such as a day of the week or a class. Like a table, a bar graph pairs each category with its value. The bars let you compare those values at a glance.

A bar graph has two axes. The category axis lists the categories, and its label says what they are. The value axis carries the scale. The scale is a set of numbers that starts at 0 and goes up in equal amounts. The scale's unit, such as minutes or dollars, tells you what the values measure. Where a bar ends on the scale is its value.

To read a bar graph, work in two parts.

Say what the bar stands for. Use its category name, the axis label and the unit. On a graph of minutes by day, the Tuesday bar stands for the minutes on Tuesday.
Read where the bar ends from the scale's numbers. If the bar ends at a number, that number is its value. If it ends between two numbers, use the number below, the number above and how much of the gap the bar reaches. A bar that ends halfway from 30 to 40 shows 35, because 35 is halfway from 30 to 40.

With the values in hand, you can compare them, subtract to find how many more, and add to find a total. Always keep the unit.

The graph below shows the minutes one student practiced piano on each school day.

Bar graph · Day

Minutes of piano practice:

30

,

45

,

35

,

20

and

40

minutes from Monday to Friday.

Worked example

Reading the practice graph

Use the graph above. Which day had the most practice, and which had the least? How many more minutes were practiced on Tuesday than on Thursday? How many minutes were practiced in all?

Say what each bar stands for. The category axis is labeled Day, so each bar is one day. The value axis is in minutes. So each bar shows the minutes practiced on its day.
Read each bar from the scale's printed numbers, not by counting lines. Look across from the end of the bar. If it ends at a printed number, that is its value. If it ends between two, use the number below, the number above and the part of the gap it reaches, as the next step shows. This gives Monday 30, Tuesday 45, Thursday 20 and Friday 40 minutes.
Wednesday's bar ends between two printed numbers. Use the number just below, the number just above and the part of that gap it reaches. If they are 30 and 40, it reaches halfway: 35. If they are 30 and 45, it reaches one third of the way: also 35. Use this method for any bar that ends between printed numbers. Wednesday shows 35 minutes.
$30 + \tfrac{1}{2}(40 - 30) = 35,\quad 30 + \tfrac{1}{3}(45 - 30) = 35$
Compare the values. Tuesday's bar is the longest and Thursday's is the shortest.
$45 > 40 > 35 > 30 > 20$
Subtract to find how many more minutes Tuesday had than Thursday. Both values are in minutes, so the difference is in minutes too.
$45 - 20 = 25$
Add all five values to find the total for the week, one bar at a time.
$30 + 45 = 75,\ 75 + 35 = 110,\ 110 + 20 = 130,\ 130 + 40 = 170$

Answer

Tuesday had the most practice ( $45$ minutes) and Thursday the least ( $20$ minutes). Tuesday had $25$ more minutes than Thursday, and the student practiced $170$ minutes in all.

To create a bar graph from a table, set up the value axis first. You make two choices:

The step: the amount, in the table's unit, that each equal space on the value axis stands for.
The number of steps from 0. Every bar starts at 0, so the top of the scale must reach the largest value. The top is the number of steps times the step.

Pick a step that keeps the number of steps easy to read. Many small steps crowd the axis. That is hard to read, but it is not wrong. A step also does not have to divide every value. If it does not, that bar ends partway through a step, between two scale values, and the graph is still correct.

Key concept

The scale turns values into bar heights

When a scale starts at 0 and goes up in equal steps, every value has a height measured in steps. To read a bar, use the scale's numbers where it ends. To create a bar, divide its value by the step to get its height in steps. The height need not be a whole number: a height of 6.5 steps ends halfway through the seventh step.

\text{height in steps} = \frac{\text{value}}{\text{step}}

Points scored in a school math contest

Class	Points scored
Class A	$60$
Class B	$90$
Class C	$70$

Worked example

Creating a graph of contest points

Create a bar graph from the table: Class A scored $60$ points, Class B scored $90$ points and Class C scored $70$ points.

Find the largest value. Class B has 90 points, so the scale must reach at least 90 points for that bar to fit.
Pick a step. A step of 10 points needs 9 steps to reach 90, which is easy to read. A step of 1 point would need 90 steps; that is correct but far too crowded to read.
$90 \div 10 = 9$
Pick the number of steps. Use 10 steps. The top is 10 times 10, or 100 points. That is more than 90, so every bar fits, and the scale ends at a round number.
$10 \times 10 = 100 \geq 90$
Find each bar's height in steps by dividing its value by the step of 10 points.
$\frac{60}{10} = 6,\quad \frac{90}{10} = 9,\quad \frac{70}{10} = 7$
Name the parts. Draw one bar for each class and label them Class A, Class B and Class C. Label the category axis Class. Give the value axis the unit points, so each bar shows one class's points.

Answer

The graph has a step of $10$ points and $10$ steps, up to $100$ points. Class A's bar is $6$ steps tall, Class B's is $9$ steps and Class C's is $7$ steps.

Bar graph · Class

The finished graph, from

0

to

100

points: Class A ends at

60

, Class B at

90

and Class C at

70

points.

Worked example

When the step does not divide every value

A class bake sale raised 40 dollars in Week 1, 65 dollars in Week 2, 100 dollars in Week 3 and 85 dollars in Week 4. Plan a bar graph: choose the scale and find each bar's height in steps.

Find the largest value. Week 3 has 100 dollars, so the scale must reach at least 100 dollars.
Compare two steps. A step of 5 dollars divides every value but needs 20 steps, which crowds the axis: hard to read, though not wrong. A step of 10 dollars needs only 10 steps. Choose 10 dollars.
$100 \div 5 = 20,\quad 100 \div 10 = 10$
Use 10 steps. The top is 10 times 10, or 100 dollars, which reaches the largest value exactly.
$10 \times 10 = 100$
Divide each value by the step of 10 dollars to find each height in steps.
$\frac{40}{10} = 4,\ \frac{65}{10} = 6.5,\ \frac{100}{10} = 10,\ \frac{85}{10} = 8.5$
Make sense of 6.5 steps. Six full steps are 60 dollars and half a step is 5 more, so Week 2's bar ends halfway from 60 to 70. Week 4's bar ends halfway from 80 to 90. The step not dividing 65 or 85 does not make the graph wrong.
$6 \times 10 + \tfrac{1}{2} \times 10 = 60 + 5 = 65$
Name the parts: bars labeled Week 1 to Week 4, a category axis labeled Week, and a value axis in dollars.

Answer

Use a step of $10$ dollars with $10$ steps, up to $100$ dollars. The bars are $4$ , $6.5$ , $10$ and $8.5$ steps tall for Weeks 1 to 4.

Takeaway: A bar graph pairs each category with a value on a scale that starts at 0. To read it, say what each bar stands for, then read where it ends from the scale's numbers, even when it ends between two of them. To create one, pick a step and enough steps to reach the largest value, then find each height as value ÷ step.

Next, you will read and interpret line graphs.