Bar Graphs Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Bar Graphs.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A chart that uses rectangular bars of different heights or lengths to represent and compare quantities, where each bar's length is proportional to the value it represents and categories are shown on one axis.

Think of buildings on a city skyline—taller buildings stand out. In a bar graph, taller bars mean bigger numbers. You can compare at a glance without reading every number.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A bar graph compares quantities with bars whose length is proportional to value, read off a numbered axis.

Common stuck point: The procedure for bar graphs is the easy part; the trap is reading every gridline as 1. Asking "Are quantities shown as bars whose height I read against a numbered axis?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Are quantities shown as bars whose height I read against a numbered axis?

Worked Examples

Example 1

easy
A bar graph shows students' favorite seasons: Spring = 5, Summer = 9, Fall = 4, Winter = 2. Which season is most popular?

Answer

Summer (9 students)

First step

1
Read each bar height: Spring=5, Summer=9, Fall=4, Winter=2.

Full solution

  1. 2
    Compare: 9 > 5 > 4 > 2.
  2. 3
    Summer has the tallest bar with 9 students.
  3. 4
    Summer is the most popular season.
In a bar graph, the tallest bar shows the largest value. We compare bar heights to find the most popular category.

Example 2

medium
A bar graph shows cookies sold each day: Mon=8, Tue=6, Wed=10, Thu=4, Fri=12. How many more cookies were sold on Friday than on Monday?

Example 3

medium
A bar graph shows favorite subjects: Math =25= 25, Science =18= 18, English =30= 30, History =22= 22. What percentage of total votes did Science receive?

Example 4

easy
A picture bar graph shows: red ★★\bigstar\bigstar, blue ★★★★★\bigstar\bigstar\bigstar\bigstar\bigstar. Which bar is taller?

Example 5

easy
A picture bar graph shows: hats ★\bigstar, shoes ★★★\bigstar\bigstar\bigstar. Which bar has fewer?

Example 6

medium
A picture bar graph shows: bees ★★★\bigstar\bigstar\bigstar, ants ★★★\bigstar\bigstar\bigstar. Are they the same?

Example 7

easy
A bar graph shows: apples 6, pears 2, plums 9. Which fruit has the tallest bar?

Example 8

easy
A bar graph shows: ducks 5, swans 5, geese 8. Which two bars are the same?

Example 9

medium
A bar graph shows: tigers 2, lions 6, bears 10. Which animal has the shortest bar?

Example 10

easy
A picture graph uses key: 1 star =1= 1 book. It shows: Sam has 7 stars, Mia has 4 stars. How many books does Sam have?

Example 11

easy
A tally chart shows for buses: two bundles of 5 plus ∣∣||. How many buses?

Example 12

hard
A tally chart shows: cars three bundles of 5 plus ∣|, trucks two bundles of 5. How many more cars than trucks?

Example 13

easy
A bar graph (scale of 2) shows: dogs reach the 9th gridline. How many dogs?

Example 14

easy
A bar graph (scale of 2) shows favorite drinks: juice at 7 gridlines, milk at 5 gridlines. How many kids chose juice?

Example 15

hard
A bar graph (scale of 5) shows: A 4 gridlines, B 9 gridlines, C 6 gridlines. Goal is 100 total. How many more are needed?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A bar graph shows: Soccer = 7, Basketball = 5, Swimming = 3. How many students were surveyed in total?

Example 2

medium
A bar graph shows library books checked out: Fiction=15, Nonfiction=9, Comics=12. How many fewer nonfiction books than fiction books were checked out?

Example 3

easy
A bar graph shows: apples 4, bananas 7, cherries 2. How many bananas?

Example 4

easy
A bar graph shows apples 4, bananas 7, cherries 2. How many more bananas than cherries?

Example 5

easy
A bar graph shows red 5, blue 8, green 3. Which color has the tallest bar?

Example 6

easy
A bar graph shows dogs 6, cats 6, birds 2. Which two categories are equal?

Example 7

easy
A bar graph shows Mon 3, Tue 5, Wed 4 books read. How many books on Tuesday?

Example 8

easy
A bar graph shows cars 8, bikes 5, buses 1. How many vehicles in total?

Example 9

easy
A bar graph shows juice 4, milk 4, water 9. Which has the shortest bar?

Example 10

easy
A bar graph's scale has each gridline = 1. A bar reaches the 6th line. What value is that?

Example 11

medium
A bar graph's scale has each gridline = 2. A bar reaches the 5th gridline. What value does it show?

Example 12

medium
A bar graph (each line = 5) shows team A at 4 lines and team B at 7 lines. How many more points has B?

Example 13

medium
A bar graph shows pets: cats 12, dogs 8, fish 6. How many more cats than the combined dogs and fish... wait, how many cats and dogs together?

Example 14

medium
A bar graph (each line = 10) shows sales: Jan 3 lines, Feb 5 lines. What were total sales for the two months?

Example 15

medium
A bar graph shows favorite seasons: spring 7, summer 10, fall 5, winter 8. How many students were surveyed?

Example 16

medium
A bar graph (each line = 2) shows a bar at 9 lines. Another bar shows a value of 16. Which is bigger?

Example 17

medium
A bar graph shows votes: A 15, B 9. If 4 voters switch from A to B, what are the new totals?

Example 18

challenge
A bar graph (each line = 5) shows a goal line at 10 lines. A bar reaches 7 lines. How many more points are needed to reach the goal?

Example 19

challenge
A bar graph shows scores 12, 18, and one missing bar. The total of all three is 45. What is the missing value?

Example 20

challenge
A bar graph (each line = 4) shows three equal bars whose values sum to 48. How many lines tall is each bar?

Example 21

medium
A bar graph shows scores 6, 9, 12, 3. What is the difference between the tallest and shortest bar?

Example 22

medium
A bar graph (each line = 3) shows a bar at 6 lines. How many does it represent?

Example 23

easy
A picture bar graph shows: dogs ★★★\bigstar\bigstar\bigstar, cats ★★\bigstar\bigstar. How many dogs?

Example 24

easy
A picture bar graph shows: apples ★★★★\bigstar\bigstar\bigstar\bigstar, bananas ★★\bigstar\bigstar. How many apples?

Example 25

easy
A picture bar graph shows: ducks ★★★★★\bigstar\bigstar\bigstar\bigstar\bigstar, fish ★★\bigstar\bigstar. How many ducks?

Example 26

easy
A picture bar graph shows: pigs ★★\bigstar\bigstar, cows ★★★\bigstar\bigstar\bigstar. How many cows?

Example 27

medium
A picture bar graph shows: cars ★★★★\bigstar\bigstar\bigstar\bigstar, bikes ★\bigstar. How many bikes?

Example 28

hard
A picture bar graph shows: balls ★★★★★\bigstar\bigstar\bigstar\bigstar\bigstar, dolls ★★★\bigstar\bigstar\bigstar. Which bar is the tallest?

Example 29

easy
A bar graph shows: dogs 5, cats 3, fish 2. How many cats?

Example 30

easy
A bar graph shows: red 8, blue 4, green 6. How many blue?

Example 31

easy
A bar graph shows: pencils 7, crayons 10, markers 3. How many crayons?

Example 32

medium
A bar graph shows: stars 4, moons 6. How many in all?

Example 33

medium
A bar graph shows favorite snacks: chips 7, cookies 3. How many more kids picked chips?

Example 34

easy
A tally chart shows: apples ∣∣∣∣ /||||\,/ (5), pears ∣∣∣||| (3). How many apples?

Example 35

easy
A tally chart shows for cats: one bundle of 5 plus ∣∣∣|||. What is the total?

Example 36

easy
A bar graph shows pets: dogs 12, cats 8. How many pets in all?

Example 37

medium
A bar graph shows favorite colors: red 9, blue 6, green 4. How many more kids chose red than green?

Example 38

medium
A tally chart shows: Mon ∣∣∣∣ / ∣∣||||\,/\,|| (7), Tue ∣∣∣∣ / ∣∣∣∣||||\,/\,|||| (9). On which day were there more?

Example 39

easy
A bar graph uses a scale where each gridline =2= 2. A bar reaches the 4th gridline. What value does it show?

Example 40

easy
A bar graph uses a scale where each gridline =5= 5. A bar reaches the 6th gridline. What value does it show?

Example 41

easy
A bar graph (scale of 5) shows: red bar at the 8th gridline, blue bar at the 3rd gridline. How many more red than blue?

Example 42

medium
A bar graph (scale of 5) shows: Mon 4 gridlines, Tue 6 gridlines. How many books in all?

Example 43

medium
A bar graph (scale of 5) shows visitors: Sat 9 gridlines, Sun 7 gridlines. How many visitors over the weekend?
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Related Concepts

CountingComparison

Background Knowledge

These ideas may be useful before you work through the harder examples.

countingcomparison