Remembered star colours

Through the telescope a real star cluster shone – dozens of stars in golden, blue and reddish colours, close together. Liri tried to count them, and stopped short. “That is how I used to watch the sky above my home, too! But all I remember is: there were far more blue stars than reddish ones…”

Erklärus: “Then we’ll reconstruct it with a tally chart. And afterwards we’ll turn it into a picture that you can understand at a glance – perhaps the exact memory will come back.”

✏️ The tally chart – counting quickly

In a tally chart you make one mark for every thing you count. The fifth mark is drawn across the other four – that makes it easier to read.

Golden:✦✦✦✦ / ✦✦
Blue:✦✦✦✦ / ✦✦✦✦
Reddish:✦✦✦
Liri: “For golden I see 5 plus 2, so 7. For blue 5 plus 5, so 10!”
How many reddish stars were counted?

📋 The frequency table

The tally chart becomes a frequency table – the marks as clear numbers:

Star colourNumber
Golden7
Blue10
Reddish3
How many stars were counted altogether (7+10+3)?

📈 Liri’s chart-builder – interactive

Enter your own values – the bar chart appears live:

📊 Build your own bar chart
🌌 Data in the universe

Astronomers use charts to sort thousands of stars by brightness and temperature – the famous Hertzsprung–Russell diagram shows at a glance how stars change over the course of their lives.
Space telescopes such as Hubble also collect huge amounts of data that only become understandable through tables and charts.

❌ Common mistake

In tally charts people often forget to draw the fifth mark across the others! Without the bundles of five, counting up at the end becomes much slower and more error-prone.

📝 Exercise 1
A tally chart shows: ✦✦✦✦ / ✦✦✦✦ / ✦ – how many marks is that altogether?
📝 Exercise 2
In a bar chart the bar for “blue” is twice as tall as the bar for “red”. Red = 4. How tall is blue?
📝 Exercise 3
A frequency table shows: Monday=3, Tuesday=5, Wednesday=2. How many altogether?

A pattern that shows the way

Liri looked at her finished bar chart – at a glance she could see which star colour appeared most often in the sky. She wrote the pattern onto her star map.

Liri: “Now I understand straight away, without counting every mark one by one! And this pattern – that is exactly what the sky above my home looked like.”
Erklärus: “That is exactly the point of charts: making big amounts of data understandable at a glance. And sometimes such a pattern holds exactly the clue you need.”
“Tally chart: quick counting, bundles of five drawn across. Frequency table: marks as numbers. Bar chart: values as rectangles for comparing.”
What you learned today
Tally chart → table → chart
Collect, sort and show data
🌟

Chapter 30 mastered!

Liri can now collect data, sort it and show it in charts.

Erklärus’s notebook – page 30:
“Tally chart for counting, frequency table for sorting, chart for understanding at a glance.”
← Back to overview 30 – Data & Charts