Statistics Toolkit (OCR GCSE Maths)

Exam Questions

3 hours55 questions

1 mark

Lee wishes to find out if there is a relationship between a person’s age and the time it takes them to complete a puzzle.

Lee decides to conduct an experiment.
She asks 12 people to complete the puzzle.
She records each person’s age and the time taken to complete the puzzle.

Make one criticism of Lee’s method.

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	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

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

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	$□$	$□$

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

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

	Boys	Girls
Number of students	102	85
Mean mark	68.5	72.4

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
$150 < x ⩽ 250$	$1$
$250 < x ⩽ 350$	$11$
$350 < x ⩽ 450$	$5$
$450 < x ⩽ 550$	$0$
$550 < x ⩽ 650$	$3$

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

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

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

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

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
$0 < h ⩽ 4$	$8$
$4 < h ⩽ 8$	$21$
$8 < h ⩽ 12$	$12$
$12 < h ⩽ 16$	$7$
$16 < h ⩽ 20$	$2$

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

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