Frequency Tables and Grouped Data

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Build the Table in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

1 - Getting Started ~4 mins

Illustration for Getting Started Here is a messy list of reaction-time scores, just numbers scattered across the board with no order at all: 7, 5, 8, 6, 7, 9, 6, 8, 7, 5, 9, 6, 7, 8, 6, 7, 5, 8, 7, 9, 6, 7, 8, 6. Take a good look at them.

Think about it

If you had to tell someone what these scores were like, what would you say? How could we tidy this mess into something we can actually make sense of?

Teacher Notes

Display the untidy raw list as pupils settle. Take two or three hands-up suggestions, not open call-out. Listen for ideas like 'put them in order' or 'count how many of each' — both are roads into a frequency table.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Illustration for Watch and Notice

Tallying the reaction-time scores: 5, 6, 7, 8, 9

Watch how we tally the messy scores from a moment ago into a frequency table. Each column header is one of the actual score values, and every time that score appears we add one stroke. Every fifth stroke crosses the previous four so we can read the totals at a glance.

Grouping ages: 0–9, 10–19, 20–29

When the values spread out too far to list one at a time, we group them into equal bands instead. Notice how each band is the same width (ten years each) and every age has exactly one home. If the bands were too narrow we would end up with dozens of them; too wide and everything would land in one band. We want a number of bands that is useful to read.

The gap trap: when bands overlap

Look carefully at these bands: 0–10 and 10–20. The number 10 belongs to both bands, so it has two homes at once. That is the trap. Bands must leave no gaps and never share a number, which is why we write 0–9 and 10–19 instead, so each value fits in exactly one group.

Teacher Notes

Walk each example aloud, one at a time.

First table — point out that the headers are the real scores (5, 6, 7, 8, 9) from the messy list, so pupils see the raw scatter turned into a tidy count. Point to the crossed-through group of five and ask the class how it speeds up reading the total.
Second table — stress that every band is the same width (ten years each). This is the make-or-break idea. Make the too-narrow / too-wide point out loud so the band-width judgement is on the board, not just in your head.
Third table — the bands shown deliberately overlap (0–10 and 10–20). Point at the value 10 and ask which band it belongs to: the answer is both, which is the problem. Then show the fix: 0–9 and 10–19. Equal AND non-overlapping.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~7 mins

Today we explore: here is a fresh set of class data — 18 scores to tally into three equal bands: 4, 11, 20, 7, 15, 22, 9, 13, 25, 6, 18, 21, 8, 14, 27, 12, 19, 24. We will agree on the band edges first, then tally each value into its band and check the totals add back to 18.

Key point

Remember the non-overlapping rule: each value has exactly one home. So does 20 go in 10–19 or 20–29? It goes in 20–29, because 10–19 stops at 19.

Tally these 18 scores into three equal bands

Teacher Notes

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

Agree the three band edges (0–9, 10–19, 20–29) before any tallying starts — pupils often jump straight to marking and then find a value with no home. Watch for the boundary value (the on-screen reminder names 20 going in 20–29) and revoice: 'each value has exactly one home.' Have a few pupils add tally marks in turn while the class checks the running total reaches 18.

+15 XP

4 - Build the Table in Your Copy ~3 mins

COPYBOOK MOMENT

Illustration for Build the Table in Your Copy In your maths copy, draw a grouped frequency table with three equal class intervals for the data we have been working with. Give it a tally column and a frequency column.

Fill in the tallies and the frequency for each band, then write the total at the bottom to check it matches the whole set.

Teacher Notes

Walk the room glancing for equal band widths and tally marks grouped in fives — this is whole-class copybook practice, not marking. A quick check that the bottom total matches the data set catches most slips.

+10 XP

5 - Class Challenge ~12 mins

Today we work through three different data sets, and we have to choose the right band width for each one. Here are the sets on the board:

Set A: 2, 5, 8, 3, 7, 9, 4, 6, 1, 8, 5, 3 (values run 1 to 9)
Set B: 12, 27, 35, 8, 19, 41, 23, 16, 38, 29, 5, 44 (values run 5 to 44)
Set C: 65, 23, 91, 48, 12, 77, 34, 88, 56, 19, 102, 71 (values run 12 to 102)

The rule today

If we choose bands that are too narrow we end up with dozens of nearly empty bands; too wide and everything lands in one. Aim for a band width that gives roughly four to six bands — enough to see the shape of the data without drowning in columns. We will decide the right interval for each set together.

Choose a band width for each set

Teacher Notes

This round is the practice bank — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.

The deciding skill this year is choosing a sensible band width for the spread of the data — too narrow and there are dozens of bands, too wide and everything lands in one. The too-narrow / too-wide tension is now on the pupils' screen, so let them reason from it. Ask each time: 'how many bands does this give us, and is that a useful number?' Aim for roughly four to six bands. Fast finishers wait quietly and predict the band edges for the next set in their head.

+15 XP

6 - What Did We Notice? ~3 mins

MATHS TALK

What do we lose when we group data into bands, and what do we gain? If someone only sees your grouped table, what can they no longer tell about the original scores?

Teacher Notes

Listen for pupils naming the trade-off: grouping makes a wide spread readable but hides the exact individual values inside each band. Revoice a strong answer: 'so we can see the shape of the data, but not the exact number any one person got.' Head off the idea that grouping is just 'tidying' — it genuinely throws information away in return for clarity.

+10 XP

7 - What's Next ~2 mins

Today's key ideas

A frequency table records how often each value or band appears, with tally marks grouped in fives for easy reading.
When values spread too widely, we group them into equal, non-overlapping class intervals.
Grouping makes data readable but hides the exact individual values, so the band width matters — aim for a width that gives roughly four to six bands.

Coming up

Next we turn frequency tables into charts, building and reading bar charts and multiple bar charts to compare two groups side by side.

Teacher Notes

A quick recap of the three key ideas closes the lesson. The bar-chart lesson that follows builds directly on the grouped tables pupils made today.

+5 XP

Pupil practice

Module 9 · Data and Chance Mixed

Lesson 93 · Frequency Tables and Grouped Data

Download Activity Book page (PDF)

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Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

Tallying the reaction-time scores: 5, 6, 7, 8, 9

Grouping ages: 0–9, 10–19, 20–29

The gap trap: when bands overlap

3 - Try It Together ~7 mins

Tally these 18 scores into three equal bands

4 - Build the Table in Your Copy ~3 mins

5 - Class Challenge ~12 mins

Choose a band width for each set

6 - What Did We Notice? ~3 mins

7 - What's Next ~2 mins

Today's key ideas

Coming up

Unlock the full learning experience

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