Lesson 19.2: Bar Graphs, Frequency Tables, and Range
Applied concepts and practical problem solving for Bar Graphs, Frequency Tables, and Range.
⏱️ Reading Time: 20 mins
• ❓ 50 Interactive Practice Questions
🌟
Real-Life Story: Data Handling and Pictographs
School Science Fair: Comparing energy savings from solar vs wind experiments across classrooms.
💡 Core Mathematical Concepts: Bar Graphs, Frequency Tables, and Range
Focus areas: Reading single and double bar charts, finding mode, and calculating data range..
| Concept / Term | Mathematical Meaning | Real-Life Application |
|---|---|---|
| Frequency Table | A structured table showing categories and counts using tally marks | Organizing raw survey data |
| Bar Graph | Bars of equal width with lengths proportional to frequencies | Vertical and horizontal charts |
| Range | Difference between the highest and lowest data values in a set | Highest value - Lowest value |
| Mode | The data category or value that appears most frequently | Most popular choice |
📝 Step-by-Step Worked Examples
Worked Example 1: Find range
Highest score is 92, lowest score is 68 -> Range = 92 - 68 = 24 marks.
Worked Example 2: Read bar height
If bar reaches 35 on y-axis, frequency is 35.
⚠️ Common Misconceptions to Avoid
Common Misconception: Confusing bar width with value
Correction: Bar height/length indicates value; bar width is always uniform and meaningless.
Common Misconception: Misreading scale intervals on the vertical axis
Correction: Check whether the y-axis counts by 2s, 5s, 10s, or 20s.
🎯
Self-Check Challenge
A library recorded daily book loans: Mon 45, Tue 60, Wed 55, Thu 75, Fri 90. What is the difference between the most and least borrowed days?
Answer & Explanation:
Highest is Friday (90), lowest is Monday (45). Difference = 90 - 45 = 45 books.
🎯 Key Learning Takeaways
Extend understanding of Bar Graphs, Frequency Tables, and Range.
Solve multi-step real-world problems systematically.
Verify solutions through mathematical reasoning.
📄 Printable Worksheets (5 Available)
Download ready-to-print PDFs for offline student practice with separate parent/teacher answer keys.
G5-M-CH19-WS05
A4 • 15 Qs
Data Handling and Pictographs: Worksheet 5
Practice Assessment 5 • Central Botanical Gardens Context
G5-M-CH19-WS04
A4 • 15 Qs
Data Handling and Pictographs: Worksheet 4
Practice Assessment 4 • Eco-Friendly Solar Park Context
G5-M-CH19-WS03
A4 • 15 Qs
Data Handling and Pictographs: Worksheet 3
Practice Assessment 3 • Harbor Marine Terminal Context
G5-M-CH19-WS02
A4 • 15 Qs
Data Handling and Pictographs: Worksheet 2
Practice Assessment 2 • Science & Discovery Museum Context
G5-M-CH19-WS01
A4 • 15 Qs
Data Handling and Pictographs: Worksheet 1
Practice Assessment 1 • City Regional Airport Context
✍️ Lesson Practice Questions (50 Questions)
Solve these real-world challenges online, test your understanding, and reveal instant step-by-step explanations.
1
Short Answer
Hard
2 Marks
In a survey of 50 students: 30 play soccer, 25 play basketball, and 12 play both sports. How many students play neither sport?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7 students
Step-by-Step Explanation:
Total playing sports = 30 + 25 - 12 = 43 students. Neither sport = 50 - 43 = 7 students.
2
Short Answer
Hard
2 Marks
A student scored 78, 82, and 88 on the first three science tests. What score must the student achieve on the fourth test to obtain an overall mean average of 85?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
92
Step-by-Step Explanation:
Total sum required = 85 × 4 = 340. Current sum = 78 + 82 + 88 = 248. Required fourth test score = 340 - 248 = 92.
3
Short Answer
Hard
2 Marks
Explain why the mean might be misleading if a data set contains one extreme outlier (such as salaries of $30k, $32k, $35k, and $1,000k).
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The extreme high value of $1,000k skews the sum, pulling the mean up to $274k, which does not represent typical earnings for most people in the group.
Step-by-Step Explanation:
Outliers distort arithmetic means; medians provide a more resilient central measure.
4
Short Answer
Hard
2 Marks
Why is a bar chart generally easier to read accurately than a pictograph when data values are not multiples of the key?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Bar charts have a continuous numerical axis where bar heights align directly with exact values, whereas pictographs require estimating fractional portions of icons.
Step-by-Step Explanation:
Continuous linear scales provide precise quantitative alignment without symbol estimation.
5
Short Answer
Medium
1 Mark
When finding the range of 5, 8, 12, 20, a student calculates 20 - 8 = 12. What was the student's mistake?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Subtracted the second number instead of the minimum value 5 (Range is 20 - 5 = 15)
Step-by-Step Explanation:
Range is maximum minus minimum: 20 - 5 = 15, not 20 - 8.
6
Short Answer
Medium
1 Mark
A student looks at a pictograph where 1 symbol = 10 apples and sees 4.5 symbols. The student writes '45 apples'. A classmate argues 'You can't have half a symbol.' Who is correct?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The student is correct (half a symbol represents 5 apples, so 4.5 × 10 = 45)
Step-by-Step Explanation:
Half symbols are standard in pictographs to represent half the key value (1/2 of 10 = 5). Total is 45.
7
Fill in the Blanks
Medium
1 Mark
Find the missing value: The mean of 12, 15, 18, and [ ? ] is 15.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
Sum must be 15 × 4 = 60. Current sum = 12 + 15 + 18 = 45. Missing = 60 - 45 = 15.
8
Fill in the Blanks
Medium
1 Mark
Pictograph Key: 1 star = 12 awards. Grade 5 won 60 awards. How many star symbols should be drawn?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5
Step-by-Step Explanation:
60 ÷ 12 = 5 stars.
9
Short Answer
Medium
1 Mark
A test score record lists 5 quiz scores: 85, 90, 75, 95, 80. Calculate the student's mean quiz score.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
85
Step-by-Step Explanation:
Sum = 85 + 90 + 75 + 95 + 80 = 425. Mean = 425 ÷ 5 = 85.
10
Short Answer
Medium
1 Mark
In a bar graph showing favorite sports among 120 fifth-graders: Soccer has 45 votes, Basketball has 35, Swimming has 25, and Tennis has the rest. How many students voted for Tennis?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15 students
Step-by-Step Explanation:
45 + 35 + 25 = 105. Remaining for Tennis = 120 - 105 = 15 students.
11
Short Answer
Medium
1 Mark
At the Central Botanical Gardens, an environmental tally counts bird species over a weekend: Sparrows (24), Robins (16), Pigeons (30), and Blue jays (10). What is the total number of birds recorded?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
80 birds
Step-by-Step Explanation:
24 + 16 + 30 + 10 = 80 birds.
12
Multiple Choice
Easy
1 Mark
What is the average (mean) of the numbers 10, 20, 30, and 40?
A
25
B
20
C
30
D
100
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
25
Step-by-Step Explanation:
Sum = 10 + 20 + 30 + 40 = 100. Mean = 100 ÷ 4 = 25.
13
Multiple Choice
Easy
1 Mark
Find the range of this data set: 12, 28, 15, 39, 21.
A
27
B
28
C
39
D
12
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
27
Step-by-Step Explanation:
Range = Maximum - Minimum = 39 - 12 = 27.
14
Multiple Choice
Easy
1 Mark
What is the mode of the following data set: 14, 18, 14, 22, 19, 14, 25?
A
14
B
18
C
19
D
25
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
14
Step-by-Step Explanation:
The mode is the most frequently occurring value. 14 appears 3 times.
15
Multiple Choice
Easy
1 Mark
In a school pictograph, each symbol of an open book represents 8 library books read. If Grade 5 has 6 book symbols, how many books were read?
A
48 books
B
40 books
C
54 books
D
14 books
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
48 books
Step-by-Step Explanation:
6 symbols × 8 books/symbol = 48 books.
16
Short Answer
Hard
2 Marks
In a survey of 50 students: 30 play soccer, 25 play basketball, and 12 play both sports. How many students play neither sport?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7 students
Step-by-Step Explanation:
Total playing sports = 30 + 25 - 12 = 43 students. Neither sport = 50 - 43 = 7 students.
17
Short Answer
Hard
2 Marks
A student scored 78, 82, and 88 on the first three science tests. What score must the student achieve on the fourth test to obtain an overall mean average of 85?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
92
Step-by-Step Explanation:
Total sum required = 85 × 4 = 340. Current sum = 78 + 82 + 88 = 248. Required fourth test score = 340 - 248 = 92.
18
Short Answer
Hard
2 Marks
Explain why the mean might be misleading if a data set contains one extreme outlier (such as salaries of $30k, $32k, $35k, and $1,000k).
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The extreme high value of $1,000k skews the sum, pulling the mean up to $274k, which does not represent typical earnings for most people in the group.
Step-by-Step Explanation:
Outliers distort arithmetic means; medians provide a more resilient central measure.
19
Short Answer
Hard
2 Marks
Why is a bar chart generally easier to read accurately than a pictograph when data values are not multiples of the key?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Bar charts have a continuous numerical axis where bar heights align directly with exact values, whereas pictographs require estimating fractional portions of icons.
Step-by-Step Explanation:
Continuous linear scales provide precise quantitative alignment without symbol estimation.
20
Short Answer
Medium
1 Mark
When finding the range of 5, 8, 12, 20, a student calculates 20 - 8 = 12. What was the student's mistake?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Subtracted the second number instead of the minimum value 5 (Range is 20 - 5 = 15)
Step-by-Step Explanation:
Range is maximum minus minimum: 20 - 5 = 15, not 20 - 8.
21
Short Answer
Medium
1 Mark
A student looks at a pictograph where 1 symbol = 10 apples and sees 4.5 symbols. The student writes '45 apples'. A classmate argues 'You can't have half a symbol.' Who is correct?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The student is correct (half a symbol represents 5 apples, so 4.5 × 10 = 45)
Step-by-Step Explanation:
Half symbols are standard in pictographs to represent half the key value (1/2 of 10 = 5). Total is 45.
22
Fill in the Blanks
Medium
1 Mark
Find the missing value: The mean of 12, 15, 18, and [ ? ] is 15.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
Sum must be 15 × 4 = 60. Current sum = 12 + 15 + 18 = 45. Missing = 60 - 45 = 15.
23
Fill in the Blanks
Medium
1 Mark
Pictograph Key: 1 star = 12 awards. Grade 5 won 60 awards. How many star symbols should be drawn?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5
Step-by-Step Explanation:
60 ÷ 12 = 5 stars.
24
Short Answer
Medium
1 Mark
A test score record lists 5 quiz scores: 85, 90, 75, 95, 80. Calculate the student's mean quiz score.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
85
Step-by-Step Explanation:
Sum = 85 + 90 + 75 + 95 + 80 = 425. Mean = 425 ÷ 5 = 85.
25
Short Answer
Medium
1 Mark
In a bar graph showing favorite sports among 120 fifth-graders: Soccer has 45 votes, Basketball has 35, Swimming has 25, and Tennis has the rest. How many students voted for Tennis?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15 students
Step-by-Step Explanation:
45 + 35 + 25 = 105. Remaining for Tennis = 120 - 105 = 15 students.
26
Short Answer
Medium
1 Mark
At the Eco-Friendly Solar Park, an environmental tally counts bird species over a weekend: Sparrows (24), Robins (16), Pigeons (30), and Blue jays (10). What is the total number of birds recorded?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
80 birds
Step-by-Step Explanation:
24 + 16 + 30 + 10 = 80 birds.
27
Multiple Choice
Easy
1 Mark
What is the average (mean) of the numbers 10, 20, 30, and 40?
A
25
B
20
C
30
D
100
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
25
Step-by-Step Explanation:
Sum = 10 + 20 + 30 + 40 = 100. Mean = 100 ÷ 4 = 25.
28
Multiple Choice
Easy
1 Mark
Find the range of this data set: 12, 28, 15, 39, 21.
A
27
B
28
C
39
D
12
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
27
Step-by-Step Explanation:
Range = Maximum - Minimum = 39 - 12 = 27.
29
Multiple Choice
Easy
1 Mark
What is the mode of the following data set: 14, 18, 14, 22, 19, 14, 25?
A
14
B
18
C
19
D
25
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
14
Step-by-Step Explanation:
The mode is the most frequently occurring value. 14 appears 3 times.
30
Multiple Choice
Easy
1 Mark
In a school pictograph, each symbol of an open book represents 8 library books read. If Grade 5 has 6 book symbols, how many books were read?
A
48 books
B
40 books
C
54 books
D
14 books
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
48 books
Step-by-Step Explanation:
6 symbols × 8 books/symbol = 48 books.
31
Short Answer
Hard
2 Marks
In a survey of 50 students: 30 play soccer, 25 play basketball, and 12 play both sports. How many students play neither sport?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7 students
Step-by-Step Explanation:
Total playing sports = 30 + 25 - 12 = 43 students. Neither sport = 50 - 43 = 7 students.
32
Short Answer
Hard
2 Marks
A student scored 78, 82, and 88 on the first three science tests. What score must the student achieve on the fourth test to obtain an overall mean average of 85?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
92
Step-by-Step Explanation:
Total sum required = 85 × 4 = 340. Current sum = 78 + 82 + 88 = 248. Required fourth test score = 340 - 248 = 92.
33
Short Answer
Hard
2 Marks
Explain why the mean might be misleading if a data set contains one extreme outlier (such as salaries of $30k, $32k, $35k, and $1,000k).
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The extreme high value of $1,000k skews the sum, pulling the mean up to $274k, which does not represent typical earnings for most people in the group.
Step-by-Step Explanation:
Outliers distort arithmetic means; medians provide a more resilient central measure.
34
Short Answer
Hard
2 Marks
Why is a bar chart generally easier to read accurately than a pictograph when data values are not multiples of the key?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Bar charts have a continuous numerical axis where bar heights align directly with exact values, whereas pictographs require estimating fractional portions of icons.
Step-by-Step Explanation:
Continuous linear scales provide precise quantitative alignment without symbol estimation.
35
Short Answer
Medium
1 Mark
When finding the range of 5, 8, 12, 20, a student calculates 20 - 8 = 12. What was the student's mistake?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Subtracted the second number instead of the minimum value 5 (Range is 20 - 5 = 15)
Step-by-Step Explanation:
Range is maximum minus minimum: 20 - 5 = 15, not 20 - 8.
36
Short Answer
Medium
1 Mark
A student looks at a pictograph where 1 symbol = 10 apples and sees 4.5 symbols. The student writes '45 apples'. A classmate argues 'You can't have half a symbol.' Who is correct?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The student is correct (half a symbol represents 5 apples, so 4.5 × 10 = 45)
Step-by-Step Explanation:
Half symbols are standard in pictographs to represent half the key value (1/2 of 10 = 5). Total is 45.
37
Fill in the Blanks
Medium
1 Mark
Find the missing value: The mean of 12, 15, 18, and [ ? ] is 15.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
Sum must be 15 × 4 = 60. Current sum = 12 + 15 + 18 = 45. Missing = 60 - 45 = 15.
38
Fill in the Blanks
Medium
1 Mark
Pictograph Key: 1 star = 12 awards. Grade 5 won 60 awards. How many star symbols should be drawn?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5
Step-by-Step Explanation:
60 ÷ 12 = 5 stars.
39
Short Answer
Medium
1 Mark
A test score record lists 5 quiz scores: 85, 90, 75, 95, 80. Calculate the student's mean quiz score.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
85
Step-by-Step Explanation:
Sum = 85 + 90 + 75 + 95 + 80 = 425. Mean = 425 ÷ 5 = 85.
40
Short Answer
Medium
1 Mark
In a bar graph showing favorite sports among 120 fifth-graders: Soccer has 45 votes, Basketball has 35, Swimming has 25, and Tennis has the rest. How many students voted for Tennis?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15 students
Step-by-Step Explanation:
45 + 35 + 25 = 105. Remaining for Tennis = 120 - 105 = 15 students.
41
Short Answer
Medium
1 Mark
At the Harbor Marine Terminal, an environmental tally counts bird species over a weekend: Sparrows (24), Robins (16), Pigeons (30), and Blue jays (10). What is the total number of birds recorded?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
80 birds
Step-by-Step Explanation:
24 + 16 + 30 + 10 = 80 birds.
42
Multiple Choice
Easy
1 Mark
What is the average (mean) of the numbers 10, 20, 30, and 40?
A
25
B
20
C
30
D
100
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
25
Step-by-Step Explanation:
Sum = 10 + 20 + 30 + 40 = 100. Mean = 100 ÷ 4 = 25.
43
Multiple Choice
Easy
1 Mark
Find the range of this data set: 12, 28, 15, 39, 21.
A
27
B
28
C
39
D
12
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
27
Step-by-Step Explanation:
Range = Maximum - Minimum = 39 - 12 = 27.
44
Multiple Choice
Easy
1 Mark
What is the mode of the following data set: 14, 18, 14, 22, 19, 14, 25?
A
14
B
18
C
19
D
25
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
14
Step-by-Step Explanation:
The mode is the most frequently occurring value. 14 appears 3 times.
45
Multiple Choice
Easy
1 Mark
In a school pictograph, each symbol of an open book represents 8 library books read. If Grade 5 has 6 book symbols, how many books were read?
A
48 books
B
40 books
C
54 books
D
14 books
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
48 books
Step-by-Step Explanation:
6 symbols × 8 books/symbol = 48 books.
46
Short Answer
Hard
2 Marks
In a survey of 50 students: 30 play soccer, 25 play basketball, and 12 play both sports. How many students play neither sport?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7 students
Step-by-Step Explanation:
Total playing sports = 30 + 25 - 12 = 43 students. Neither sport = 50 - 43 = 7 students.
47
Short Answer
Hard
2 Marks
A student scored 78, 82, and 88 on the first three science tests. What score must the student achieve on the fourth test to obtain an overall mean average of 85?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
92
Step-by-Step Explanation:
Total sum required = 85 × 4 = 340. Current sum = 78 + 82 + 88 = 248. Required fourth test score = 340 - 248 = 92.
48
Short Answer
Hard
2 Marks
Explain why the mean might be misleading if a data set contains one extreme outlier (such as salaries of $30k, $32k, $35k, and $1,000k).
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The extreme high value of $1,000k skews the sum, pulling the mean up to $274k, which does not represent typical earnings for most people in the group.
Step-by-Step Explanation:
Outliers distort arithmetic means; medians provide a more resilient central measure.
49
Short Answer
Hard
2 Marks
Why is a bar chart generally easier to read accurately than a pictograph when data values are not multiples of the key?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Bar charts have a continuous numerical axis where bar heights align directly with exact values, whereas pictographs require estimating fractional portions of icons.
Step-by-Step Explanation:
Continuous linear scales provide precise quantitative alignment without symbol estimation.
50
Short Answer
Medium
1 Mark
When finding the range of 5, 8, 12, 20, a student calculates 20 - 8 = 12. What was the student's mistake?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Subtracted the second number instead of the minimum value 5 (Range is 20 - 5 = 15)
Step-by-Step Explanation:
Range is maximum minus minimum: 20 - 5 = 15, not 20 - 8.