Start with the recap, study the fully worked examples, then use the practice problems to
check your understanding of Bar Graph.
This page combines explanation, solved examples, and follow-up practice so you can move
from recognition to confident problem-solving in Statistics.
Concept Recap
A bar graph is a chart that uses rectangular bars of different heights or lengths to compare quantities across distinct categories. Each bar represents one category, and the bar's length is proportional to the value it represents.
Think of bar graphs as a competition where categories show off their numbers by how tall their bars stand. The taller the bar, the bigger the number. You can instantly see the winner without doing any math!
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:Bar Graph organizes data so the right pattern is visible without distorting the counts or scale.
Common stuck point:Students often know a procedure related to bar graph but skip the recognition step: Am I choosing or interpreting a display that matches the type of data and the question being asked? That leads to a calculation or graph that looks reasonable but answers a different question.
Sense of Study hint:Ask: Am I choosing or interpreting a display that matches the type of data and the question being asked?
Worked Examples
Example 1
easy
A bar graph shows votes for class president: A 10, B 7, C 3. Walk through how to find the total votes.What is the total number of votes?
Answer
20
First step
1
Read each bar: A is 10, B is 7, C is 3.
See the full worked solution + why-it-works coaching
Setup·Key insight·Why it works·Common pitfall·Connection
A bar graph of donations ($) shows A=60,B=90,C=120,D=30. What percent of the total came from B?What percent of the total came from B?
Example 3
hard
A bar graph of 5 bars has mean 12. Four bars are 10,14,8,15. What is the fifth bar?The mean of the 5 bars is 12. Four bars are known. What is the fifth?
Example 4
easy
The favourite fruits of 20 students are: Apple (7), Banana (5), Orange (4), Grape (4). Draw a bar graph and determine which fruit is most popular.
Example 5
medium
A bar graph shows book genres read by students: Fiction (12), Non-fiction (8), Mystery (10), Sci-fi (6), Biography (4). How many students were surveyed in total, and what fraction chose Mystery?
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easy
A bar graph shows bars of height 6, 4, and 9. What is the tallest bar's value?Which bar is tallest?
Example 2
easy
Two bars have heights 8 and 5. How much taller is the first?How much taller is Bar 1 than Bar 2?
Example 3
easy
A bar graph has bars 3, 3, 3, 3. What is the total of all bars?What is the total of all four bars?
Example 4
easy
A bar graph shows category counts 7, 2, 6, 5. What is the smallest value?What is the smallest value?
Example 5
easy
Which fits categories best: a bar graph or a single number? Answer 1 for bar graph, 2 for single number.
Example 6
easy
A bar graph shows 5 and 10 for two categories. What is the combined total?What is the combined total of both bars?
Example 7
easy
A bar graph must start its value axis at zero to be honest. If a bar reaches 12 on a zero-based axis, what value does it show?
Example 8
easy
Bars show 4, 8, and 4. What is the total?What is the total of all three bars?
Example 9
medium
A bar graph shows 12, 8, 15, 5. What is the difference between the tallest and shortest bars?What is the difference between the tallest and shortest bars?
Example 10
medium
A bar graph of 4 categories has heights 6, 9, 12, 9. What is the mean height?What is the mean height of the four bars?
Example 11
medium
A bar graph shows total 50 across 5 bars, with four bars at 8, 12, 10, and 11. What is the fifth bar's height?Four bars are known (8, 12, 10, 11) and the total is 50. What is the fifth bar?
Example 12
medium
A bar graph of 60 responses shows category A at 24. What fraction is A? Give a simplified fraction.
Example 13
medium
On a bar graph with gridlines every 5 units, a bar reaches the 7th gridline above zero. What value does it show?
Example 14
medium
Two bars are in ratio 3:5 and the taller is 25. What is the shorter bar's height?
Example 15
challenge
A bar graph's axis wrongly starts at 10. A bar drawn from 10 to 40 appears to be 3 times another bar from 10 to 20. What is the true ratio of their values (taller to shorter)?
Example 16
challenge
A bar graph has 5 bars whose heights are consecutive even numbers summing to 40. What is the tallest bar?
Example 17
challenge
A bar graph shows categories A, B, C where B is 4 more than A and C is double B. If the total is 40, what is C?
Example 18
medium
A bar graph of 5 bars totals 60; four bars are 10, 14, 12, and 13. What is the fifth bar's height?Four bars are known (10, 14, 12, 13) and the total is 60. What is the fifth bar?
Example 19
medium
On a bar graph with gridlines every 4 units, a bar reaches the 6th gridline. What value does it show?
Example 20
medium
A bar graph of 4 bars has heights 10, 14, 8, 12. What is the mean height?What is the mean height of the four bars?
Example 21
easy
A bar graph shows fruit sales: apples 14, bananas 9, cherries 6. How many apples were sold?How many apples were sold?
Example 22
easy
A bar graph shows four bars with heights 5,8,6,1. How many bars are taller than 5?How many bars are taller than 5?
Example 23
easy
A bar graph has bars of heights 3,6,9,12. By how much does each successive bar grow?By how much does each successive bar grow?
Example 24
easy
A bar graph shows weekly book sales: 20,25,30. What is the total?What is the total across all three weeks?
Example 25
easy
A bar graph shows colors picked: red 9, blue 9, green 4. What is the mode?What is the mode of the color data?
Example 26
medium
A bar graph shows monthly rainfall (cm): Jan 4, Feb 6, Mar 8, Apr 2. What is the mean monthly rainfall?What is the mean monthly rainfall?
Example 27
medium
A bar graph of 4 categories has total 80 with three known bars 25,18,22. What is the missing bar's height?Three bars are known (25, 18, 22) and the total is 80. What is the missing bar?
Example 28
medium
A bar graph of 40 surveys shows 14 people picking 'pizza'. What percent of respondents chose pizza?
Example 29
medium
A bar graph shows test scores grouped by class: 9th 72, 10th 80, 11th 77, 12th 83. What is the difference between highest and lowest mean?What is the difference between the highest and lowest class mean?
Example 30
medium
A double bar graph compares boys vs. girls choosing sports: soccer 10/8, basketball 7/9, tennis 4/5. In how many sports do girls outnumber boys?
Example 31
medium
A bar graph shows bars 20,30,40,10. What is the ratio of the largest bar to the smallest?What is the ratio of the largest bar to the smallest?
Example 32
medium
A bar graph shows visits: Mon 40, Tue 50, Wed 60, Thu 50, Fri 80. What is the median?What is the median of the daily visit counts?
Example 33
medium
A bar graph shows car colors of 200 cars: red 60, blue 50, black 40, white 50. What fraction (simplified) is red?
Example 34
hard
A bar graph's bars are a,2a,3a,4a and the total is 60. What is a?
Example 35
hard
A bar graph shows scores rounded to nearest 5: A=20,B=25,C=15,D=30. After a 20% increase in all bars, what is the new total?After a 20% increase in all bars, what is the new total?
Example 36
hard
A bar graph compares incomes of 4 neighborhoods: $40k,$60k,$50k,$70k. After Neighborhood D rises by $30k, what is the new mean?After D rises by $30k, what is the new mean income?
Example 37
hard
A bar graph shows 4 months with heights forming an arithmetic sequence with first term 5 and common difference 4. What is the total?What is the total of the four bars in arithmetic sequence?
Example 38
hard
A stacked bar graph shows total revenue for a store as products: A \$120, B \$80, C \$200, with returns reducing A by \$30 and C by \$20. What is the net revenue?
Example 39
challenge
A bar graph of 5 bars has total 50 and median (after sorting) 11. If the smallest two bars are equal, the fourth bar is 12, and the largest is 15, what is the value of each of the two smallest bars?
Example 40
easy
A bar graph shows the number of rainy days in four months: Jan (10), Feb (7), Mar (5), Apr (8). Which month had the fewest rainy days, and how many more rainy days did January have than March?
Example 41
easy
A bar graph shows votes for class captain: Maya 18, Leo 12, Sam 15, and Priya 9. How many votes were cast in total, and how many more votes did Maya receive than Priya?