Grade 10 Data Representation: Short Notes

10 ශ්‍රේණිය · 10 පරිච්ඡේදය · දත්ත නිරූපණය

91%

of Grade 10 term tests include it (49 of 54)

519

marks in past papers (60 questions)

9 min

full lesson with quick checks

🎯 What you'll learn

Find sector angles from data or from a ratio
Draw a pie chart with a protractor and label it
Find a missing sector angle
Find amounts and totals from a pie chart
Solve problems when the data in a pie chart change

Where did the money go?

A school in Galle collected Rs 72,000 for its sports meet. The principal wants parents to see, at one glance, how much went to prizes, food, tents and sound. A long list of numbers won't do it. One circle cut into slices will: a pie chart.

What a pie chart shows

A pie chart shows how a whole is shared into parts.• The full circle stands for the total.• The angle at the centre is 360°.• Each part gets a sector whose angle at the centre is in proportion to its amount.A bigger share gets a bigger angle. Use it to compare parts of one whole, not to show change over time.

🧮 Finding a sector angle

Shortcut: first find the angle for one unit, 360° ÷ total, then multiply by each amount. Always check that all the angles add up to 360°.

Sector angle = (amount ÷ total) × 360°

✏️ How 40 students get to school

In a Grade 10 class of 40 in Kurunegala, 18 come by bus, 10 walk, 8 come by three-wheeler and 4 cycle. Find the sector angles for a pie chart.

1One student = 360° ÷ 40 = 9°.
2Bus 18 × 9° = 162°; walk 10 × 9° = 90°.
3Three-wheeler 8 × 9° = 72°; bicycle 4 × 9° = 36°.
4Check: 162 + 90 + 72 + 36 = 360 ✓

✅ 162°, 90°, 72°, 36°

Drawing it

Draw a circle and one radius. Measure 162° from it with a protractor and draw the next radius; measure the next angle from that line, and so on. Label each sector (bus, walk, three-wheeler, bicycle) or add a key.

Reading a pie chart backwards

Exams usually give the angles and ask for amounts.Amount = (angle ÷ 360°) × totalIf the total is not given, use a sector you know: find the amount for 1°, then multiply.Example: a 40° sector stands for 36 buses, so 1° = 36 ÷ 40 = 0.9 bus, and the whole chart = 0.9 × 360 = 324 vehicles.

✏️ A family budget

A pie chart shows a family's monthly spending. Food is 120°, education 72°, transport 60°, and the rest is savings. Education is Rs 14,400. Find (i) the savings angle (ii) the total (iii) the amount spent on food.

1(i) Savings = 360 − (120 + 72 + 60) = 108°.
2(ii) 72° is Rs 14,400, so 1° is Rs 200.
3Total = 200 × 360 = Rs 72,000.
4(iii) Food = 200 × 120 = Rs 24,000.

✅ (i) 108° (ii) Rs 72,000 (iii) Rs 24,000

⚠️ Missing sector first

In O/L papers many candidates tried to use an unknown sector before finding its angle, or forgot that the angles make 360°. If a sector has no angle written, find it first: 360° minus the others. Also look for the small square that marks a 90° sector.

⚠️ When the data changes

If Rs 10,000 more is given to one part, that part grows and so does the total. A common slip is to keep the old total. Recalculate: new angle = new amount ÷ new total × 360°. The other sectors shrink a little even though their amounts did not change.

📌 Remember

• The whole circle (360°) is the total.• Sector angle = amount ÷ total × 360°; check the angles add to 360°.• From a ratio: 360° ÷ total parts gives one part.• Reading a chart: find the amount for 1° from a known sector, then multiply.• Find any missing angle first; if the data change, the total changes too.

🧾 Quick revision sheet

Angles at the centre of a pie chart add up to…	360°
Sector angle formula	Angle = amount ÷ total × 360°
Amount from a sector angle	Amount = angle ÷ 360° × total
A sector of 90° is what fraction of the whole?	One quarter (1/4).
Ratio 2 : 3 : 4. One part is how many degrees?	360° ÷ 9 = 40°
40 people in total. Angle for one person?	360° ÷ 40 = 9°
What is a pie chart best for?	Comparing the parts of one whole.