Sec 1 · G2 (N(A))

Statistics

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1. Collecting and organising data

Mode of transport	Tally	Frequency
Bus	$\cancel{\|\|\|\|}\ \cancel{\|\|\|\|}\ \cancel{\|\|\|\|}\ \|\|\|$	$18$
MRT	$\cancel{\|\|\|\|}\ \cancel{\|\|\|\|}\ \cancel{\|\|\|\|}\ \cancel{\|\|\|\|}\ \|\|\|\|$	$24$
Car	$\cancel{\|\|\|\|}\ \|\|\|\|$	$9$
Walk	$\cancel{\|\|\|\|}\ \|\|\|\|$	$9$
Total		$60$

📖 Worked example

The bar graph shows the favourite hawker food of a class. Find how many more pupils there are for Satay than for Nasi lemak.

Step 1 of 2

Work out what one small division stands for, then read the two bars

One small division stands for

20

.Satay:

380

; Nasi lemak:

180

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2. Pie charts and bar graphs

The 60 pupils as a pie chart (Bus 108°, MRT 144°, Car 54°, Walk 54°) and as a bar graph with bars of 18, 24, 9 and 9.

Angle for Bus: 18 out of 60

\displaystyle \dfrac{18}{60} \times 360^\circ

e.g.

\displaystyle \dfrac{18}{60} \times 360

\displaystyle = 108

From an angle back to a number: Car is 54°

\displaystyle \dfrac{54}{360} \times 60

e.g.

\displaystyle \dfrac{54}{360} \times 60

\displaystyle = 9

📖 Worked example

The table shows the CCAs chosen by Secondary 1 pupils. The information is to be shown in a pie chart. Calculate the angle of the sector for Uniformed.

Item	Uniformed	Sports	Arts	Clubs
Number of pupils	42	27	32	19

Step 1 of 2

Find the total

\text{Total} = 42 + 27 + 32 + 19

= 120

📖 Worked example

The line graph shows the monthly sales of a bubble tea shop. Find the sales in Apr.

Step 1 of 1

Work out what one small division stands for. Go up from Apr to the line, then across to the axis

At Apr, the sales was

6

thousand cups.

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3. Misleading graphs

Look for	Why it misleads
vertical axis not starting at $0$	small differences look large
picture made wider and taller	doubling both makes the area $4$ times
uneven gaps on a time axis	the rate of change is distorted: equal distances on the axis are not equal times
bars of different widths	the wider bar looks bigger
no key or scale	values cannot be read

📖 Worked example

The number of cars sold went up from $150$ in 2019 to $300$ in 2023, which is $2$ times as many. The artist drew the 2023 picture $2$ times as tall and $2$ times as wide as the 2019 picture. The area of the 2023 picture is $k$ times the area of the 2019 picture. Find the value of $k$ .

Step 1 of 1

Area grows with BOTH the height and the width

2 \times 2

= 4

The picture looks

4

times as big, though the number is only

2

times as large.

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4. Choosing a statistical diagram

Diagram	Best for	Limitation
Pictogram	small counts, shown with pictures and a key	part of a symbol is hard to read exactly
Bar graph	comparing separate categories	does not show each part's share of the whole
Line graph	change over time (the trend)	values between the plotted points are only estimates
Pie chart	each part as a share of the whole	no actual numbers unless the total is given

📖 Worked example

The pie chart shows the fruit sold at a stall. Which statement does the pie chart support?

Step 1 of 2

Check each statement against the diagram: true, false or can't tell

The Oranges and Apples sectors together are more than half of the pie.

141^\circ + 84^\circ = 225^\circ

against

180^\circ

. True.There are 28 fruits for Apples. The total is not given: a pie chart alone gives fractions of the whole but not numbers. Can't tell.There are 84 fruits for Apples. The total is not given: a pie chart alone gives fractions of the whole but not numbers. Can't tell.The Durians and Mangoes sectors together are more than half of the pie.

72^\circ + 63^\circ = 135^\circ

against

180^\circ

. False.

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Sec 1 · G2 (N(A))

Statistics

Practise statistics with step-by-step help. Free account.

Start free

1. Collecting and organising data

Mode of transport	Tally	Frequency
Bus	$\cancel{\|\|\|\|}\ \cancel{\|\|\|\|}\ \cancel{\|\|\|\|}\ \|\|\|$	$18$
MRT	$\cancel{\|\|\|\|}\ \cancel{\|\|\|\|}\ \cancel{\|\|\|\|}\ \cancel{\|\|\|\|}\ \|\|\|\|$	$24$
Car	$\cancel{\|\|\|\|}\ \|\|\|\|$	$9$
Walk	$\cancel{\|\|\|\|}\ \|\|\|\|$	$9$
Total		$60$

📖 Worked example

The bar graph shows the favourite hawker food of a class. Find how many more pupils there are for Satay than for Nasi lemak.

Step 1 of 2

Work out what one small division stands for, then read the two bars

One small division stands for

20

.Satay:

380

; Nasi lemak:

180

Practise this →

2. Pie charts and bar graphs

Angle for Bus: 18 out of 60

\displaystyle \dfrac{18}{60} \times 360^\circ

e.g.

\displaystyle \dfrac{18}{60} \times 360

\displaystyle = 108

From an angle back to a number: Car is 54°

\displaystyle \dfrac{54}{360} \times 60

e.g.

\displaystyle \dfrac{54}{360} \times 60

\displaystyle = 9

📖 Worked example

The table shows the CCAs chosen by Secondary 1 pupils. The information is to be shown in a pie chart. Calculate the angle of the sector for Uniformed.

Item	Uniformed	Sports	Arts	Clubs
Number of pupils	42	27	32	19

Step 1 of 2

Find the total

\text{Total} = 42 + 27 + 32 + 19

= 120

📖 Worked example

The line graph shows the monthly sales of a bubble tea shop. Find the sales in Apr.

Step 1 of 1

Work out what one small division stands for. Go up from Apr to the line, then across to the axis

At Apr, the sales was

6

thousand cups.

Practise this →

3. Misleading graphs

Look for	Why it misleads
vertical axis not starting at $0$	small differences look large
picture made wider and taller	doubling both makes the area $4$ times
uneven gaps on a time axis	the rate of change is distorted: equal distances on the axis are not equal times
bars of different widths	the wider bar looks bigger
no key or scale	values cannot be read

📖 Worked example

Step 1 of 1

Area grows with BOTH the height and the width

2 \times 2

= 4

The picture looks

4

times as big, though the number is only

2

times as large.

Practise this →

4. Choosing a statistical diagram

Diagram	Best for	Limitation
Pictogram	small counts, shown with pictures and a key	part of a symbol is hard to read exactly
Bar graph	comparing separate categories	does not show each part's share of the whole
Line graph	change over time (the trend)	values between the plotted points are only estimates
Pie chart	each part as a share of the whole	no actual numbers unless the total is given

📖 Worked example

The pie chart shows the fruit sold at a stall. Which statement does the pie chart support?

Step 1 of 2

Check each statement against the diagram: true, false or can't tell

The Oranges and Apples sectors together are more than half of the pie.

141^\circ + 84^\circ = 225^\circ

against

180^\circ

72^\circ + 63^\circ = 135^\circ

against

180^\circ

. False.

Practise this →

Practise statistics with step-by-step help

Endless questions from basic to exam level. Get one wrong and see where it went wrong. Free account.

Start free