Statistics

Statistics is the study of collecting, organising and interpreting information (data). At Key Stage 1, statistics appears in Year 2, where children begin making simple charts and asking questions about data.

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What This Topic Covers

Year 2 (statistics is not in Year 1):

• Interpret and construct pictograms, tally charts, block diagrams and tables
• Ask and answer questions by counting objects in each category
• Sort categories by quantity
• Compare data totals

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What is Data?

Data is information collected about something. In Year 2, children collect data about things they can count and sort:

Examples of data children might collect:

• Favourite colours in the class
• Pets owned by classmates
• How children travel to school
• Favourite fruits or sports

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Tally Charts

A tally chart is a quick way to count and record data. Each mark (tally) represents one item. After four tallies, a fifth mark crosses through them to make a group of 5 — making counting easier.

Tally symbols:

• 1 = |
• 2 = ||
• 3 = |||
• 4 = ||||
• 5 = |||| (four vertical marks with one diagonal cross-mark)

Example — How do children travel to school?

Travel method	Tally	Total
Walk
Car
Bus
Bike
Scooter

Total children: 9 + 8 + 5 + 3 + 2 = 27

flowchart LR
  A[Ask a question] --> B[Collect answers]
  B --> C["Tally chart<br/>marks in groups of 5"]
  C --> D["Pictogram<br/>one picture per child"]
  C --> E["Block diagram<br/>one block per child"]
  D --> F[Read and compare]
  E --> F

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Pictograms

A pictogram uses pictures or symbols to represent data. Each symbol stands for a certain number of items.

Example — Favourite fruit (each symbol = 1 child):

Fruit	Symbols	Count
Apple	[apple][apple][apple][apple]	4
Banana	[banana] x 6	6
Orange	[orange] x 3	3
Strawberry	[strawberry] x 5	5

In Year 2, children also begin working with pictograms where each symbol represents more than 1 item (e.g. each picture = 2 children). This is called many-to-one correspondence.

Example with many-to-one (each paw print = 2 children):

Pet	Symbols	Count
Dog	[paw][paw][paw]	6
Cat	[paw][paw][paw][paw][paw]	10
Fish	[paw][paw]	4
None	[paw][paw][paw][paw]	8

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Block Diagrams (Block Graphs)

A block diagram uses columns of blocks to show the frequency of each category. Each block typically represents one item.

Example — Favourite sports:

Number
of
children
7 | X
6 | X
5 | X         X
4 | X         X
3 | X     X   X
2 | X     X   X   X
1 | X     X   X   X
  +-------+---+---+--------
  Football Tennis Swimming Gymnastics

Football = 7, Tennis = 3, Swimming = 5, Gymnastics = 2

Reading a block diagram:

• The height of each bar shows the total for that category
• The scale on the left shows the numbers

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Tables

Tables organise data in rows and columns, making it easy to compare.

Example — Number of books read per month:

Month	Books read
January	5
February	7
March	4
April	6
May	8

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Asking and Answering Questions

Once data is displayed, children ask and answer questions about it:

Question type	Example
How many?	How many children walk to school?
Which is most popular?	Which fruit was chosen most?
Which is least popular?	Which sport was chosen least?
How many altogether?	How many children answered the survey?
How many more?	How many more chose football than tennis?
How many fewer?	How many fewer chose gymnastics than swimming?

Example using the travel to school data:

• How many children walk? 9
• Which is the most popular way to travel? Walk (9 children)
• How many more children come by car than by bus? 8 - 5 = 3
• How many children were surveyed altogether? 9 + 8 + 5 + 3 + 2 = 27

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Key Vocabulary

Term	Meaning
data	information collected about something
tally chart	a chart using marks to count items
pictogram	a chart using pictures to represent data
block diagram	a chart using blocks/bars to show quantities
table	data organised in rows and columns
category	a group things can be sorted into
frequency	how often something occurs
total	the combined count
most popular	the category with the highest count
least popular	the category with the lowest count
many-to-one	each symbol represents more than one item

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Common Misconceptions

• "Every symbol in a pictogram = 1" — Once many-to-one correspondence is introduced, children must check the key before interpreting a pictogram.
• "The tallest bar is always the most important" — The most important is whatever the question asks about. Sometimes you need the shortest bar.
• "Data must be about numbers" — Data can be categorical (e.g. favourite colour) or about non-numeric information.
• "Half a block in a block diagram means half a thing" — When working with whole numbers, children should not have half-blocks. If they appear, check the scale.

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Worked Example for Parents and Teachers

Imagine you are running a class survey on "Which fruit do you bring in your lunchbox?" with a Year 2 group of 24 children. Statistics in KS1 is best taught as a complete cycle: collect, record, represent, interpret. Walk children through each stage explicitly so they see how raw information becomes a chart they can read.

Step 1 — Collecting the data (concrete). Hand each child a sticky note. Ask them to write their fruit and place the note on a category sign on the floor (apple, banana, orange, grapes, none). The columns of sticky notes form a physical block diagram before any drawing happens. Stand back with the class and ask, "Which column is tallest?" — children can see frequency before they can read it.

Step 2 — Recording with tallies. On a flipchart, draw a tally chart with the categories down the left. Walk along the line of children and mark a tally for each. Model the gate of five carefully: say, "One, two, three, four — now I cross to make a gate, that is five." This is a common pinch-point: children draw a fifth vertical line instead of a diagonal cross. Demonstrate the difference and have them practise in the air with their finger.

Step 3 — Moving to a pictogram (pictorial). Use printed fruit symbols. Start with one-to-one correspondence: each apple sticker = 1 child. Then introduce many-to-one with a key: "Today each apple stands for two children." Ask, "If we have 6 children who chose apple, how many stickers do we need?" (3). Use a half symbol to represent a single odd child if needed, and discuss why the key matters.

Step 4 — Block diagram (abstract). Draw axes on squared paper. The vertical axis shows the count, the horizontal axis shows the categories. Each block is one square high. Verbalise as you draw: "Apple has 6, so I colour 6 squares up."

Verbal prompts to use throughout:

• "What does this chart tell us?"
• "Which is the most popular? How do you know?"
• "How many more chose banana than orange? Show me how to work that out."
• "How many altogether? What addition do we need?"

Common errors to watch for:

• Mis-counting tallies because the gate is drawn incorrectly.
• Forgetting to look at the key on a many-to-one pictogram.
• Reading bars without checking the scale on the vertical axis.
• Confusing most and least, or more and fewer.
• Adding rather than subtracting when comparing two categories.

Encourage children to write a short sentence underneath their chart: "The most popular fruit was apple. Eight more children chose apple than orange." This connects statistics to writing for a real purpose.

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Misconception Callout