Statistics
Carroll diagrams and tally charts
In this unit you sort things two different ways. A Carroll diagram sorts by whether things have a feature or not. A tally chart helps you count things quickly in fives.
Carroll diagrams
A Carroll diagram sorts objects by whether they have or do not have a feature. One box is for things that have the feature, like 'Triangles'. The other box is for things that do not, like 'Not triangles'. You can sort numbers too, such as 'Even' and 'Not even', or 'More than 10' and 'Not more than 10'.
Tally marks
A tally chart uses marks called tallies. One mark stands for one object. The marks are grouped in fives. When you reach the fifth mark, you cross it through the first four. This makes a group of five that is easy to count.
Counting a tally
Count the groups of five first, then add the extra single marks. One group of 5 and 3 more single marks is 5 + 3 = 8. Counting in fives makes adding up a big tally chart quick.
Comparing the data
Once you have counted, you can compare. The most common thing has the biggest number. The least common has the smallest number. To find how many more or fewer, subtract the two numbers.
Worked examples
Sort a number in a Carroll diagram
- The boxes are 'Even' and 'Not even'.
- Look at the number 12.
- 12 is an even number.
Answer: 12 goes in the 'Even' box.
Count a tally
- There is one full group of 5.
- There are 3 more single marks.
- Add them: 5 + 3 = 8.
Answer: The tally shows 8.
Read a tally chart
- Cars have 3 full groups of 5.
- Count in fives: 5, 10, 15.
- So there are 15 cars.
Answer: There are 15 cars.
Compare two amounts
- Fruit has 14 and crisps has 4.
- To find how many fewer crisps, subtract.
- 14 - 4 = 10.
Answer: There are 10 fewer crisps than fruit.
Where you see this in real life
- Using a tally chart to count how many cars, buses and vans pass the school.
- Sorting animals into a Carroll diagram by whether they have spots or not.
- Making a tally chart to record which number a dice lands on.
Key words
- Carroll diagram
- A chart that sorts things by whether they have a feature or not.
- Tally
- A mark that stands for one object.
- Tally chart
- A chart of tally marks used to count things quickly.
- Data
- Information you collect, such as how many of each thing there are.
- Most common
- The thing with the biggest number.
- Least common
- The thing with the smallest number.