Statistics Toolkit (AQA GCSE Maths)

Exam Questions

3 hours55 questions

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2 marks

Naga states a hypothesis.

“Most people read more than 100 books a year.”

She asks a sample of five people in a book club how many books they read last month.
The table shows the results.

	Lynn	Ali	Paul	Chen	Ruth
Number of books	10	11	8	10	13

Show how Naga could use the data to support her hypothesis.

How did you do?

2 marks

Give two reasons why this sample should not be used to support her hypothesis.

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Injury time, $t$ (minutes)	Frequency
$0 < t ⩽ 2$	59
$2 < t ⩽ 4$	158
$4 < t ⩽ 6$	106
$6 < t ⩽ 8$	45
$8 < t ⩽ 10$	12

Day	1	2	3	4	5	6	7	8	9	10
Number of planes	148	151	147	155	153	147	155	102	151	154

	Median	Interquartile range	Range
Men	28	7.5	31
Women	30	9	37

Number of minutes late, $t$	Number of trains
$0 ⩽ t < 2$	12
$2 ⩽ t < 4$	0
$4 ⩽ t < 6$	7
$6 ⩽ t < 8$	0
$8 ⩽ t < 10$	0
$10 ⩽ t < 12$	1

Time, $t$ (minutes)	Frequency
$0 < t ⩽ 20$	1
$20 < t ⩽ 40$	6
$40 < t ⩽ 60$	3

	True	False
The mean could be less than 20 minutes	$□$	$□$
The mean could be more than 40 minutes	$□$	$□$
The mean could be less than 40 minutes	$□$	$□$

The range could be more than 40 minutes	$□$	$□$
The range could be less than 40 minutes	$□$	$□$
The range could be more than 60 minutes	$□$	$□$

	Median	Interquartile range
Science	$27$	$18$
Maths	$24.5$	$11$

Weight of parcel ( $p$ kg)	Frequency
$0 < p ⩽ 1$	19
$1 < p ⩽ 2$	12
$2 < p ⩽ 3$	5
$3 < p ⩽ 4$	2
$4 < p ⩽ 5$	2

Speed (s kilometres per hour)	Frequency
$40 < s ⩽ 50$	10
$50 < s ⩽ 60$	16
$60 < s ⩽ 70$	19
$70 < s ⩽ 80$	23
$80 < s ⩽ 90$	12

Length of time ( $t$ minutes)	Frequency
$0 < t ⩽ 10$	4
$10 < t ⩽ 20$	10
$20 < t ⩽ 30$	15
$30 < t ⩽ 40$	25
$40 < t ⩽ 50$	6

Dress size	Number of women
$8$	$2$
$10$	$9$
$12$	$8$
$14$	$6$

Median	70
Lower quartile	54
Upper quartile	73
Least age	42
Greatest age	85

Time, $t$ minutes	Number of people
$0 < t ⩽ 5$	3
$5 < t ⩽ 10$	9
$10 < t ⩽ 15$	11
$15 < t ⩽ 20$	17

	Boys	Girls
Number of students	102	85
Mean mark	68.5	72.4

Time, t (mins)	Frequency	Midpoint
$0 ⩽ t < 30$	24
$30 ⩽ t < 50$	76
$50 ⩽ t < 60$	52
$60 ⩽ t < 90$	48
	Total = 200

Number of bedrooms	Number of houses
1	7
2	$a$
3	$b$
4	$c$
5	8

Height( $h$ metres)	Frequency
$1.30 ⩽ h < 1.40$	$11$
$1.40 ⩽ h < 1.50$	$9$
$1.50 ⩽ h < 1.60$	$7$
$1.60 ⩽ h < 1.70$	$6$
$1.70 ⩽ h < 1.80$	$2$

Weekly earnings( $£ x$ )	Frequency
$150 < x ⩽ 250$	$1$
$250 < x ⩽ 350$	$11$
$350 < x ⩽ 450$	$5$
$450 < x ⩽ 550$	$0$
$550 < x ⩽ 650$	$3$

Foot length( $f$ cm)	Number of adults
$16 ⩽ f < 18$	$3$
$18 ⩽ f < 20$	$6$
$20 ⩽ f < 22$	$10$
$22 ⩽ f < 24$	$12$
$24 ⩽ f < 26$	$9$

Distance, $x$ (miles)	Frequency
$0 < x ⩽ 5$	20
$5 < x ⩽ 10$	48
$10 < x ⩽ 15$	30
$15 < x ⩽ 20$	22
	Total = 120

Time taken ( $t$ minutes)	Number of customers
$0 < t ⩽ 3$	6
$3 < t ⩽ 6$	10
$6 < t ⩽ 9$	6
$9 < t ⩽ 12$	2
$12 < t ⩽ 15$	1

Speed (s mph)	Number of vehicles
$0 < s ⩽ 20$	5
$20 < s ⩽ 40$	8
$40 < s ⩽ 50$	37
$50 < s ⩽ 60$	47
$60 < s ⩽ 80$	3

Time taken ( $t$ minutes)	Frequency
$0 < t ⩽ 10$	54
$10 < t ⩽ 20$	50
$20 < t ⩽ 40$	44
$40 < t ⩽ 80$	20

Time taken (m minutes)	Frequency
$0 < m ⩽ 10$	$3$
$10 < m ⩽ 20$	$8$
$20 < m ⩽ 30$	$11$
$30 < m ⩽ 40$	$9$
$40 < m ⩽ 50$	$9$

Time ( $t$ minutes)	Frequency
$60 < t ⩽ 90$	$10$
$90 < t ⩽ 120$	$14$
$120 < t ⩽ 150$	$9$
$150 < t ⩽ 180$	$5$
$180 < t ⩽ 210$	$2$

Height( $h$ metres)	Frequency
$0 < h ⩽ 4$	$8$
$4 < h ⩽ 8$	$21$
$8 < h ⩽ 12$	$12$
$12 < h ⩽ 16$	$7$
$16 < h ⩽ 20$	$2$

Belt size	Waist( $w$ inches)	Frequency
Small	$28 < w ⩽ 32$	$24$
Medium	$32 < w \leq 36$	$12$
Large	$36 < w \leq 40$	$8$
Extra Large	$40 < w \leq 44$	$6$

Place	Number of students
Theme Park	10
Theatre	5
Sports Centre	8
Seaside	7

Statistics Toolkit (AQA GCSE Maths)

Exam Questions

1. Number

Number Toolkit

Prime Factors, HCF & LCM

Powers, Roots & Standard Form

Fractions

Percentages

Simple & Compound Interest, Growth & Decay

Fractions, Decimals & Percentages

Rounding, Estimation & Bounds

Surds

Using a Calculator

2. Algebra

Algebra Toolkit

Algebraic Roots & Indices

Expanding Brackets

Factorising

Completing the Square

Algebraic Fractions

Rearranging Formulae

Algebraic Proof

Linear Equations

Solving Quadratic Equations

Simultaneous Equations

Iteration

Forming & Solving Equations

Functions

Coordinate Geometry

Linear Graphs y = mx + c

Graphs of Functions

Equation of a Circle

Estimating Gradients & Areas under Graphs

Real-Life Graphs

Solving Inequalities

Graphing Inequalities

Transformations of Graphs

Sequences

3. Ratio, Proportion & Rates of Change

Ratio Toolkit

Ratio Problem Solving

Direct & Inverse Proportion

Standard & Compound Units

Exchange Rates & Best Buys

4. Geometry & Measures

Geometry Toolkit

Angles in Polygons & Parallel Lines

Bearings, Scale Drawing, Constructions & Loci

Circle Theorems

Area & Perimeter

Circles, Arcs & Sectors

Volume & Surface Area

Congruence, Similarity & Geometrical Proof

Area & Volume of Similar Shapes

Right-Angled Triangles - Pythagoras & Trigonometry

Sine, Cosine Rule & Area of Triangles

3D Pythagoras & Trigonometry

Vectors

Transformations

5. Probability

Probability Toolkit

Simple Probability Diagrams

Tree Diagrams

Combined & Conditional Probability

6. Statistics

Statistics Toolkit

Statistical Diagrams

Histograms

Cumulative Frequency & Box Plots

Scatter Graphs & Correlation