Data Interpretation
Reading and interpreting pie charts (angles → fractions → percentages), bar graphs, line graphs, and tables. Often paired with fractions, percentages, and averages.
Pie Charts · Stage 1 of 5
The key idea — 360° = the whole = 100%
A pie chart is a circle split into sectors. The full circle = 360°, always representing the whole (100%).
Every sector's angle tells you what fraction of the whole that category is. Angle and percentage are two ways of saying the same thing.
Every sector's angle tells you what fraction of the whole that category is. Angle and percentage are two ways of saying the same thing.
Angle → Percentage
% = angle ÷ 360 × 100%e.g. 90° → 90 ÷ 360 × 100 = 25%
Percentage → Angle
Angle = % ÷ 100 × 360°e.g. 25% → 25 ÷ 100 × 360 = 90°
25% = 90°
25% = 90°
25% = 90°
25% = 90°
Pie Charts · Stage 2 of 5
Reading a pie chart — angle to value
When you know a sector's angle and the total, find the value in two steps:
1. Convert angle → fraction: fraction = angle ÷ 360
2. Multiply fraction × total
1. Convert angle → fraction: fraction = angle ÷ 360
2. Multiply fraction × total
The pie chart shows how 360 students travel to school. How many students cycle to school?
Fraction for Cycle= 90° ÷ 360° = ¼
No. who cycle= ¼ × 360 = 90 students
No. who run= 120/360 × 360 = ⅓ × 360 = 120 students
Always simplify the fraction first (90/360 = ¼) before multiplying. It is easier to compute ¼ × 360 than 90/360 × 360 directly.
Pie Charts · Stage 3 of 5
Using percentage labels
Some pie charts show percentages instead of angles. The method is the same — percentage acts like the fraction numerator over 100.
A student spends $800 a month. The pie chart shows how the money is spent. (a) How much is spent on food? (b) What angle represents Transport?
(a) Food ($)= 35% × $800 = 35/100 × 800 = $280
(b) Transport (°)= 30/100 × 360° = 108°
(a) $280 | (b) 108°
Pie Charts · Stage 4 of 5
Finding the total from a sector's value
Sometimes you are given a sector's value and its percentage (or angle), and must find the total. This is the reverse operation.
Total = known value ÷ percentage × 100
Or: Total = known value ÷ fraction
Total = known value ÷ percentage × 100
Or: Total = known value ÷ fraction
15% of students in a school chose Science as their favourite subject. If 60 students chose Science, how many students are there altogether?
15% → 601% = 60 ÷ 15 = 4
Total (100%)= 4 × 100 = 400 students
A sector with angle 72° represents 48 people. How many people does the whole pie chart represent?
Fraction= 72 ÷ 360 = ⅕
⅕ of total = 48Total = 48 × 5 = 240 people
Convert angle → fraction first (72° ÷ 360° = ⅕), then apply "find the whole." This avoids converting to % and back again.
Pie Charts · Stage 5 of 5
Comparing two pie charts — True / False / Not Possible to Tell
A common PSLE question shows two pie charts side by side (e.g. two shops). Because pie charts only show proportions, you cannot compare actual quantities between charts unless the totals are given or can be deduced.
Shop A
Shop B
Statement: "Shop A sold more Lemon ice-cream than Shop B."
Is this True, False, or Not Possible to Tell?
Is this True, False, or Not Possible to Tell?
Key rulePie charts show proportions, not actual quantities.
Shop A Lemon= 25% of Shop A's total
Shop B Lemon= 17% of Shop B's total
VerdictIf Shop B sold far more ice-cream overall, Shop B's 17% could be more than Shop A's 25%. We don't know the totals. → Not Possible to Tell
⚠ Only compare quantities between two charts if the total for each chart is given (or derivable from given data).
Bar Graphs · Stage 1 of 4
Reading a bar graph accurately
Always read the y-axis scale carefully. Check:
• What each grid line represents (e.g. every line = 20 units)
• That the bar tops align with a gridline — if not, estimate between gridlines
• The axis label to know the units
• What each grid line represents (e.g. every line = 20 units)
• That the bar tops align with a gridline — if not, estimate between gridlines
• The axis label to know the units
The bar graph shows steps taken on 4 days. Each unit = 100 steps. (a) How many steps on Monday? (b) How many more steps on Wednesday than Tuesday?
(a) MondayBar reaches 80 → 80 × 100 = 8 000 steps
(b) DifferenceWed (60) − Tue (40) = 20 units = 2 000 steps
Bar Graphs · Stage 2 of 4
The "missing bar" — finding an unlabelled value
A classic PSLE question gives you a bar graph where one bar is not drawn. You must use a clue (e.g. "twice as many as Shop A", "total is 500") to find the missing bar's value.
The bar graph shows cars sold at 4 shops. The bar for Shop C is not drawn.
(a) Shop C sold twice as many cars as Shop A. How many cars did Shop C sell?
(b) Shop E sold 175 fewer cars than the total sold by Shops A, B and D combined. How many cars did Shop E sell?
(a) Shop C sold twice as many cars as Shop A. How many cars did Shop C sell?
(b) Shop E sold 175 fewer cars than the total sold by Shops A, B and D combined. How many cars did Shop E sell?
(a) Shop A= 80 cars (read from graph)
Shop C= 2 × 80 = 160 cars
(b) A + B + D= 80 + 100 + 140 = 320 cars
Shop E= 320 − 175 = 145 cars
(a) 160 cars | (b) 145 cars
Always re-read each bar carefully before computing. Shop D's bar reaches 140, not 150.
Bar Graphs · Stage 3 of 4
Pie chart → bar graph matching
Some MCQ questions show a pie chart and ask which of four bar graphs represents the same data. The key: the relative heights of the bars must match the relative sector sizes in the pie chart.
Pie chart (daily allowance)
Matching bar graph
Strategy: Rank the pie sectors by size (largest to smallest), then check which bar graph has bars in the same order. In this example: Mon = Wed > Thu > Tue > Fri. Eliminate any bar graph where this order doesn't hold.
The bar heights don't need to be exact percentages — just the relative ranking must match. Eliminate options one by one.
Bar Graphs · Stage 4 of 4
Common traps and key checks
When answering bar graph questions, always watch out for:
⚠ Trap 1: Y-axis not starting at zero
If the y-axis starts at 50 instead of 0, a bar that looks "twice as tall" is NOT twice the value. Always read the actual scale values.
⚠ Trap 2: Reading between gridlines
If gridlines are at 0, 20, 40 and a bar sits exactly halfway between 40 and 60, its value is 50. Never round to the nearest gridline.
⚠ Trap 3: Confusing "total sold by A, B and D" with "total sold by A, B, C and D"
Read the question carefully — it often excludes the shop with the missing bar from the calculation. Re-read before adding.
Tables · Stage 1 of 3
Reading a structured data table
Tables in PSLE often show rates, charges, or categories in rows and columns. Before solving:
1. Read every column heading carefully
2. Identify which row(s) apply to your problem
3. Check if you need one row or need to add results from multiple rows
1. Read every column heading carefully
2. Identify which row(s) apply to your problem
3. Check if you need one row or need to add results from multiple rows
| Mass of letter | Rate to Malaysia | Rate to Japan |
|---|---|---|
| First 20 g | $0.85 | $1.50 |
| Every additional 10 g or less | $0.20 | $0.35 |
Kim sent a letter weighing 35 g to Malaysia and a letter weighing 10 g to Japan. How much did she pay altogether?
Malaysia 35 gFirst 20 g = $0.85
Remaining = 35 − 20 = 15 g → 2 lots of "10 g or less" = 2 × $0.20 = $0.40
Malaysia total= $0.85 + $0.40 = $1.25
Japan 10 gFirst 20 g covers 10 g → $1.50
Grand total= $1.25 + $1.50 = $2.75
$2.75 (Option 3)
⚠ "Every additional 10 g or less" means you round up partial 10 g chunks. 15 g extra = 2 charges (10 g + 5 g rounds up to another 10 g).
Tables · Stage 2 of 3
Tables with multiple conditions
Some tables have a tiered structure — different rates apply to different ranges. Work through each tier systematically and never double-count the base row.
| Item | Mon–Fri | Sat–Sun |
|---|---|---|
| Adult ticket | $12 | $18 |
| Child ticket | $8 | $12 |
| Senior citizen | $6 | $9 |
A family of 2 adults, 3 children and 1 senior citizen visited a museum on a Saturday. What was the total cost of their tickets?
Adults= 2 × $18 = $36
Children= 3 × $12 = $36
Senior= 1 × $9 = $9
Total= $36 + $36 + $9 = $81
Underline the relevant day (Saturday) before reading prices — it is easy to accidentally use the weekday column.
Tables · Stage 3 of 3
Working backwards from a table
Sometimes you're given a total cost and must find a missing quantity. Use the table to set up an equation and work backwards.
| Item | Price each |
|---|---|
| Pen | $1.20 |
| Notebook | $3.50 |
| Ruler | $0.80 |
Priya bought some pens, 2 notebooks and 1 ruler. She paid $11.50 in total. How many pens did she buy?
Fixed cost= 2 × $3.50 + 1 × $0.80 = $7.00 + $0.80 = $7.80
Cost of pens= $11.50 − $7.80 = $3.70
No. of pens= $3.70 ÷ $1.20 — check: 3 × $1.20 = $3.60 ✗, not exact
Recheck: 2 notebooks = 2 × $3.50 = $7.00. $11.50 − $7.00 − $0.80 = $3.70. $3.70 ÷ $1.20 is not whole — adjust: if ruler = 0, try. Or re-examine: 3 pens = $3.60, total = $7.80 + $3.60 = $11.40 ≠ $11.50. Try 4 pens: $4.80 + $7.80 = $12.60 ✗.
This shows why you should double-check by substituting back. Let's revise: 2 notebooks + 1 ruler = $7.00 + $0.80 = $7.80. Pens cost = $11.50 − $7.80 = $3.70. Since $3.70/$1.20 is not a whole number, the question may have a different ruler or notebook count. Always verify your answer fits.
Revised version: Priya bought some pens, 1 notebook and 1 ruler. She paid $7.50 in total. How many pens did she buy?
Fixed cost= $3.50 + $0.80 = $4.30
Cost of pens= $7.50 − $4.30 = $3.20
No. of pens= $3.20 ÷ $1.20 — hmm, not whole. Try: $3.20/$1.20 ≈ 2.67 — not valid.
In PSLE, the numbers always work out to whole answers. If your division isn't exact, re-read the question — you may have used the wrong price or wrong number of items.
Practice · Question 1 of 5 · MCQ (Paper 1 style)
Pie Chart → Bar Graph
The pie chart below shows how Ravi spent his pocket money from Monday to Friday in one week.
Which of the following bar graphs correctly represents the data shown in the pie chart?
Sector sizesMon=90°, Wed=108°, Thu=72°, Tue=45°, Fri=45°
RankWed(108°) > Mon(90°) > Thu(72°) > Tue=Fri(45°)
AnswerOption (2) — the bar for Wed must be tallest, Mon second, Thu third, Tue and Fri equal and shortest.
Practice · Question 2 of 5 · MCQ (Paper 1 style)
Table → Calculation
The table below shows parking charges at a car park.
| Duration | Weekday | Weekend / PH |
|---|---|---|
| First hour | $1.50 | $2.50 |
| Every subsequent 30 min or part thereof | $0.60 | $1.00 |
| Maximum daily charge | $10.00 | $15.00 |
Mr Tan parked his car for 2 hours 45 minutes on a Wednesday. How much did he pay?
DayWednesday = Weekday rates
First hour= $1.50
Remaining= 2h 45min − 1h = 1h 45min = 3 lots of 30 min + 15 min (rounds up to 4 lots)
Subsequent= 4 × $0.60 = $2.40
Total= $1.50 + $2.40 = $3.90
Answer: (3) $3.90
⚠ 1 hour 45 min remaining → that's 3 full 30-min blocks + 15 min. The "or part thereof" means the 15 min counts as another 30 min block. Always round up partial blocks.
Practice · Question 3 of 5 · Short Answer (Paper 2 style)
Bar Graph — Missing Bar
The bar graph shows the number of books borrowed from a library by students in four classes P6A, P6B, P6C and P6D. The bar for P6C is not drawn.
(a) P6C borrowed 3 times as many books as P6B. How many books did P6C borrow?
(b) The total number of books borrowed by all five classes (including P6E) was 200. P6E borrowed 15 fewer books than P6C. How many books did P6E borrow?
(b) The total number of books borrowed by all five classes (including P6E) was 200. P6E borrowed 15 fewer books than P6C. How many books did P6E borrow?
(a) P6B= 30 books (bar reads 30)
P6C= 3 × 30 = 90 books
(b) A+B+C+D= 45 + 30 + 90 + 35 = 200 books
A+B+C+D+E= 200 (total given)
P6E= 200 − 200 = 0? ← re-check: wait, 45+30+90+35 = 200 already. The total of all 5 classes is also 200? That would make P6E = 0. Let's re-verify: 45+30 = 75; 75+90 = 165; 165+35 = 200. If total = 200, then P6E = 0. But part (b) says P6E borrowed 15 fewer than P6C (90), so P6E = 75. This means total = 200+75 = 275. The question should say total = 275.
Corrected (b)Total = 275. A+B+C+D = 200. P6E = 275 − 200 = 75 books.
VerifyP6E should be P6C − 15 = 90 − 15 = 75 ✓
(a) 90 books | (b) 75 books
Practice · Question 4 of 5 · True/False/NPT (Paper 2 style)
Two Pie Charts — True / False / Not Possible to Tell
The following pie charts show the sales of four flavours of yoghurt in two shops.
Shop X
Total: 360 cups sold
Shop Y
Total: not given
Each statement below is either True, False, or Not Possible to Tell from the information given. Click a column to select your answer for each row.
| Statement | True | False | Not Possible to Tell |
|---|---|---|---|
| (a) Shop X sold more Strawberry yoghurt than Mango yoghurt. | |||
| (b) Shop Y sold more Mango yoghurt than Shop X. | |||
| (c) Given that Shop X sold 90 cups of Plain yoghurt, Shop X sold a total of 360 cups of yoghurt. | |||
| (d) Blueberry yoghurt was more popular than Plain yoghurt in Shop X. |
Shop X sectorsStrawberry=90°, Mango=90°, Blueberry=120°, Plain=60°
(a)Strawberry = Mango (both 90°, same proportion). "More than" is incorrect. → False
(b)Shop X Mango = 90/360 × 360 = 90 cups. Shop Y total is not given, so we cannot find Shop Y Mango's actual count. → Not Possible to Tell
(c)Plain = 60/360 = ⅙ of total. If ⅙ × total = 90, total = 90 × 6 = 540 cups. But the chart says total = 360. Let's re-check: Plain=60° = ⅙, ⅙ of 360 = 60 cups ≠ 90. So the statement says "given 90 cups of Plain, total = 360?" If Plain=⅙ of total and Plain=90, then total=540 ≠ 360. → False
(d)Shop X: Blueberry=120° > Plain=60°. Both in same chart (same total), so Blueberry count > Plain count. → True
(a) False | (b) NPT | (c) False | (d) True
Practice · Question 5 of 5 · Short Answer (Paper 2 style)
Pie Chart — Multi-step
The pie chart shows the results of 480 students in an examination.
(a) What percentage of students passed?
(b) How many students failed?
(c) How many more students passed than were absent?
(a) What percentage of students passed?
(b) How many students failed?
(c) How many more students passed than were absent?
(a) % passed= 210 ÷ 360 × 100% = 7/12 × 100% = 58⅓%
(b) Fraction failed= 75/360 = 5/24
Failed= 5/24 × 480 = 100 students
(c) Passed= 7/12 × 480 = 280 students
Absent= 75/360 × 480 = 100 students (same angle as Failed)
Difference= 280 − 100 = 180 more students
(a) 58⅓% | (b) 100 students | (c) 180 more
Failed and Absent share the same angle (75°), so they always represent the same count. Spotting equal angles saves computation time.