Statistics

Many-to-One Data Displays

1

Read a Picture Graph (1 symbol = 2)

Each picture represents 2 students. Read the graph and answer.

Walking
Car
Bus
Bicycle
1

How many students walk to school? (Each star = 2)

2

How many more students go by car than by bus?

3

How many students were surveyed in total?

2

Read a Picture Graph (1 symbol = 5)

Each picture represents 5 items. Read the graph and answer.

Apples
Bananas
Grapes
Watermelon
1

How many apples were sold? (Each symbol = 5)

2

Which fruit sold the most?

3

How many more bananas were sold than watermelons?

3

Read a Picture Graph (1 symbol = 10)

Each picture represents 10 people.

Summer
Autumn
Winter
Spring
1

How many people prefer summer? (Each symbol = 10)

2

Which season is least popular?

3

How many people were surveyed in total?

4

Understanding the Key (Set A)

Circle the correct answer.

If each symbol = 2, and there are 5 symbols, the total is:

5
7
10

If each symbol = 5, and there are 4 symbols, the total is:

9
20
45

If each symbol = 10, and there are 3 symbols, the total is:

13
30
300
5

Understanding the Key (Set B)

Circle the correct answer.

To show 15 with symbols worth 5 each, you need:

1 symbol
3 symbols
5 symbols

To show 20 with symbols worth 2 each, you need:

5 symbols
10 symbols
20 symbols

To show 40 with symbols worth 10 each, you need:

2 symbols
4 symbols
8 symbols
6

Choose the Best Display (Set A)

Circle the best way to display each type of data.

Favourite colours of 200 students

Picture graph (1 = 10)
Tally chart
List

Daily temperature for a week

Picture graph
Line graph
Tally chart

Number of pets in each house

Picture graph (1 = 1)
Bar chart
Pie chart
7

Choose the Best Display (Set B)

Circle the best display.

Favourite sports of 50 students

Column graph
Number line
Tally only

How a student spends their day (percentages)

Bar chart
Pie chart
Picture graph

Books read by each class (6 classes)

Dot plot
Bar graph
Line graph
8

Sort: Good or Bad Display Choice?

Sort each data-display combination.

Favourite animals → bar chart
Temperature over time → pie chart
Class pets → picture graph
Height of students → line graph
Good choice
Not the best choice
9

Symbols Needed (1 symbol = 2)

How many symbols are needed to show each total? Each symbol = 2.

10
5
?
8
?
4
14
7
?
6
?
3
10

Symbols Needed (1 symbol = 5)

How many symbols for each total? Each symbol = 5.

20
4
?
35
?
7
15
3
?
50
?
10
11

Match Data to Best Graph Type

Draw a line to match.

Favourite foods (categorical)
Temperature over a week
Pets owned (small numbers)
How time is spent in a day
Line graph
Pie chart
Bar chart
Picture graph
12

Read and Answer (Picture Graph)

A picture graph shows library books borrowed. Each symbol = 5 books.

Monday: 3 symbols = ___ books

Tuesday: 5 symbols = ___ books

Wednesday: 2 symbols = ___ books

Which day had the most books borrowed?

How many books were borrowed in total?

13

Why Many-to-One?

Circle the best answer.

We use many-to-one (1 symbol = many) when:

Numbers are very small
Numbers are very large
There are only 2 categories

If data goes up to 100, a good key might be:

1 symbol = 1
1 symbol = 10
1 symbol = 100

If 1 symbol = 5 and you have 17 items, you need:

3 symbols
3 and a bit symbols
4 symbols
14

Create a Tally Chart from Data

Create tally marks for this data about favourite seasons.

ItemTallyTotal
Summer
Autumn
Winter
Spring
15

Many-to-One Picture Graph – Pets (Set A)

Each symbol = 5 pets. Use the graph to answer.

Dog
Cat
Fish
Bird
1

How many dogs does the graph show? (Remember: each symbol = 5)

2

How many cats?

3

How many more dogs than birds?

4

How many pets in total?

16

Many-to-One Picture Graph – Snacks (Set B)

Each symbol = 10 snacks. Answer the questions.

Apple
Banana
Grapes
Watermelon
1

How many bananas were sold? (Each symbol = 10)

2

How many apples?

3

Which snack was most popular?

4

How many snacks were sold altogether?

17

Many-to-One – Transport (Set C)

Each symbol = 2 students. Answer the questions.

Walk
Car
Bus
Bike
1

How many students walk? (Each symbol = 2)

2

How many travel by car?

3

How many more car travellers than bus travellers?

4

How many students in total?

18

Interpret Many-to-One Scales (Set A)

If each symbol = 5, circle the correct answer.

3 symbols means:

3
15
8

7 symbols means:

7
12
35

Half a symbol means:

0.5
2.5
5

To show 20 items you need:

2 symbols
4 symbols
20 symbols
19

Interpret Many-to-One Scales (Set B)

If each symbol = 10, circle the correct answer.

4 symbols means:

4
40
14

Half a symbol means:

0.5
5
10

To show 35 items you need:

3 symbols
3 and a half symbols
4 symbols

6 symbols means:

6
16
60
20

Interpret Many-to-One Scales (Set C)

If each symbol = 2, circle the correct answer.

5 symbols means:

5
7
10

Half a symbol means:

0.5
1
2

To show 9 items you need:

4 symbols
4 and a half symbols
5 symbols

8 symbols means:

8
16
10
21

Match Symbols to Values (Key: 1 symbol = 5)

Draw a line from each number of symbols to the value.

2 symbols
4 symbols
6 symbols
half a symbol
3 symbols
15
2.5
10
30
20
22

Match Symbols to Values (Key: 1 symbol = 10)

Draw a line to match.

1 symbol
3 symbols
5 symbols
half a symbol
7 symbols
50
10
5
30
70
23

Choose the Right Key

Sort each data set: what key should the picture graph use?

Data: 4, 6, 8, 10
Data: 15, 25, 30, 45
Data: 20, 40, 50, 80
1 symbol = 2
1 symbol = 5
1 symbol = 10
24

Many-to-One Calculations (Key = 5)

Total items = number of symbols × 5. Find the missing value.

25
5
?
40
?
5
15
3
?
50
?
5
35
7
?
25

Many-to-One Calculations (Key = 10)

Total items = number of symbols × 10. Find the missing value.

30
3
?
60
?
10
80
8
?
50
?
10
100
10
?
26

Read and Answer (Picture Graph – Set B)

A picture graph shows favourite sports. Each symbol = 5 students.

Soccer: 4 symbols = ___ students

Cricket: 3 symbols = ___ students

Swimming: 6 symbols = ___ students

Tennis: 2 symbols = ___ students

How many students were surveyed?

27

Read and Answer (Picture Graph – Set C)

A picture graph shows books read by each class. Each symbol = 10 books.

Year 3: 5 symbols = ___ books

Year 4: 7 symbols = ___ books

Year 5: 4 and a half symbols = ___ books

Which year read the most books?

How many more books did Year 4 read than Year 3?

28

Create a Tally Chart – Animals Spotted

Record tally marks for animals spotted at the zoo.

ItemTallyTotal
Kangaroo
Koala
Emu
Wombat
29

Create a Tally Chart – Lunch Orders

Record the lunch orders.

ItemTallyTotal
Sandwich
Pie
Sushi
Wrap
30

Why Many-to-One? (Set B)

Circle the best answer.

When data values are large (e.g. 50, 100, 150), using 1 symbol = 1 would:

Be easy
Need too many symbols
Be more accurate

A good key for data up to 50 might be:

1 symbol = 1
1 symbol = 5
1 symbol = 100

Half a symbol in a many-to-one display means:

Half the key value
Zero
The key value
31

Many-to-One Sequences (Key = 5)

If each symbol = 5, continue the count.

5
10
15
20
?
?
?
10
20
30
40
?
?
?
32

From Tally to Picture Graph (Set A)

Look at this tally chart. Create a picture graph where each symbol = 5.

ItemTallyTotal
Cricket
Swimming
Tennis
Football
33

From Tally to Picture Graph (Set B)

Tally chart data. Create a picture graph where each symbol = 2.

ItemTallyTotal
Red
Blue
Green
Yellow
34

Create a Many-to-One Picture Graph (Set A)

Use the data to create a picture graph where each symbol represents 2.

Data: Red = 8, Blue = 6, Green = 10, Yellow = 4. Draw your picture graph:

Draw here

Write a key for your graph:

Write one question someone could answer from your graph:

35

Create a Many-to-One Picture Graph (Set B)

Create a picture graph where each symbol = 5.

Data: Dogs = 15, Cats = 20, Fish = 10, Birds = 5. Draw your graph:

Draw here

Write the key:

Write two questions about your graph:

36

Choosing the Right Scale

Answer these questions about choosing the scale.

You have data: 10, 20, 30, 40. Would 'each symbol = 2' or 'each symbol = 10' be better? Why?

What if the data was 3, 7, 5, 9? Why might 'each symbol = 1' be the best choice?

37

Half Symbols

Sometimes we need half a symbol.

If each symbol = 4, how do you show 6? (Hint: 1 full + half)

If each symbol = 10, how do you show 25? Draw it:

Draw here
38

Collect Data and Create a Display

Plan and create your own data display.

What question will you investigate?

Collect or make up data for at least 4 categories:

Draw a many-to-one picture graph. State your key:

Draw here

Write 3 questions about your graph:

39

Challenge: Critique a Data Display

Think critically about data displays.

A picture graph uses 'each symbol = 3' but one category has 7 items. What is the problem?

Why is it important to include a key on a many-to-one graph?

40

Home Activity: Data Displays

Create data displays at home!

  • 1Survey your family about favourite dinners. Make a picture graph where each symbol = 2 votes.
  • 2Count cars that pass your house in 15 minutes. Group by colour and make a picture graph.
  • 3Look at a graph in a newspaper or online. What does each symbol represent?
  • 4Collect data about something you are interested in and choose the best way to display it.
41

Books Read This Month (Many-to-One, Scale 5)

Each book icon = 5 books. Read the pictograph and answer the questions.

Year 3
Year 4
Year 5
Year 6
1

How many books did Year 4 read?

2

Which year group read the most books?

3

What is the total number of books read?

4

How many more books did Year 6 read than Year 3?

42

Sports Participation (Scale 10)

Each whistle icon = 10 students. Read the graph and answer.

Football
Swimming
Tennis
Cricket
Gymnastics
1

How many students play football?

2

Which sport has the most participants?

3

How many students play tennis or gymnastics combined?

4

How many students were surveyed altogether?

43

Choose the Right Scale

Decide on the best scale for each dataset.

Data: 30, 50, 70, 90, 110 students. What scale would you use for a pictograph? (e.g., 1 icon = ___ students)

Data: 450, 600, 350, 750, 500 cars. Best scale: 1 icon = ___ cars. Why?

What scale would be misleading? Give an example.

44

Read a Bar Graph

Answer questions about a bar graph where each bar represents data.

A bar graph shows pets owned: cats 35, dogs 50, fish 20, birds 15. What type of graph would show this best?

The y-axis goes from 0 to 60 in steps of 10. What is the value halfway between 30 and 40?

How many more dogs than cats are owned according to the data?

45

Favourite Fruit Survey Results

25 students voted. Read the tally and answer the questions below.

ItemTallyTotal
Apple
Banana
Watermelon
Grapes
46

Interpreting Many-to-One Displays

Circle the correct answer.

A pictograph uses 1 car icon = 4 cars. There are 6 icons. How many cars?

6
10
24

A bar graph scale is 0 to 100 by 20s. A bar reaches halfway between 60 and 80. Value?

65
70
75

A pictograph shows 3.5 icons. Each icon = 10 students. How many students?

35
30
40

Which scale for a pictograph showing values 40, 80, 120, 160?

Scale = 1
Scale = 10
Scale = 100
47

Creating a Pictograph

Use the data to plan a pictograph.

Data: Cats 60, Dogs 80, Fish 40, Rabbits 20. Choose scale = ___. Number of icons for each: Cats ___, Dogs ___, Fish ___, Rabbits ___

Would a scale of 1 = 60 work? Why or why not?

48

Comparing Data Displays

Answer these questions about different ways to display data.

What are two advantages of using a pictograph over a tally chart?

What are two advantages of using a bar graph over a pictograph?

When would a tally chart be better than a graph?

49

Collecting and Displaying Data

Plan your own data collection and display.

What question would you ask to collect data from your class?

How many possible answers (categories) would there be?

What display type and scale would you choose? Why?

50

Misleading Graphs

Think critically about data displays.

A graph shows ice cream sales. The y-axis starts at 800, not 0. How does this make the graph misleading?

Two classes vote for their favourite sport. Class A has 30 students, Class B has 20. If we use a tally, are the results directly comparable? Why/why not?

51

Line Graphs

Line graphs show data that changes over time. Answer these questions.

Temperature at 8am = 14°C, 10am = 18°C, 12pm = 24°C, 2pm = 26°C, 4pm = 22°C. During which 2-hour period did temperature rise the most?

What does a line going steeply upward on a line graph mean?

What does a horizontal line on a line graph mean?

52

Challenge: Design a Survey

Design a complete data collection and display project.

Survey question: ___. Response options: ___

Collect responses from at least 5 people and record with tallies.

Plan your pictograph: scale = ___, icons per category: ___

Write two conclusions from your data.