Level A Level Exam Board Edexcel Subject Mathematics Module Mechanics and Statistics Topic Location and spread Sub-Topic Coding data Booklet Question paper 1 Coding data Question Paper 1 45 minutes /38 /100 Time Allowed: Score: Percentage: For more awesome resources, visit us at www.savemyexams.co.uk/ 1 A* A B C D E U >85% 77.5% 70% 62.5% 57.5% 45% <45% Grade Boundaries:
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Level A Level
Exam Board Edexcel
Subject Mathematics
Module Mechanics and Statistics
Topic Location and spread
Sub-Topic Coding data
Booklet Question paper 1
Coding dataQuestion Paper 1
45 minutes
/38
/100
Time Allowed:
Score:
Percentage:
For more awesome resources, visit us at www.savemyexams.co.uk/
1
A* A B C D E U
>85% 77.5% 70% 62.5% 57.5% 45% <45%
Grade Boundaries:
A company manager is investigating the time taken, t minutes, to complete an aptitude test.The human resources manager produced the table below of coded times, x minutes, for a random sample of 30 applicants.
Coded time (x minutes) Frequency (f )
Coded time midpoint ( y minutes)
0 ≤ x < 5 3 2.5
5 ≤ x < 10 15 7.5
10 ≤ x < 15 2 12.5
15 ≤ x < 25 9 20
25 ≤ x < 35 1 30
(You may use ∑fy = 355 and ∑f y 2 = 5675)
(2) (a) Use linear interpolation to estimate the median of the coded times.
(b) Estimate the standard deviation of the coded times.(2)
The company manager is told by the human resources manager that he subtracted 15 from each of the times and then divided by 2, to calculate the coded times.
(c) Calculate an estimate for the median and the standard deviation of t .(3)
The following year, the company has 25 positions available. The company manager decides not to offer a position to any applicant who takes 35 minutes or more to complete the aptitude test.
The company has 60 applicants.
(d) Comment on whether or not the company manager’s decision will result in the companybeing able to fill the 25 positions available from these 60 applicants. Give a reason foryour answer.
(Total 9 marks)
(2)
1.
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2
The marks, x, of 45 students randomly selected from those students who sat a mathematicsexamination are shown in the stem and leaf diagram below.
The mean and standard deviation of the marks of all the students who sat the examination were 55 and 10 respectively. The examiners decided that the total mark of each student should be scaled by subtracting 5 marks and then reducing the mark by a further 10 %.
Find the mean and standard deviation of the scaled marks of all the students.(4)
Key (3|6 means 36)
(Total 4 marks)
2.
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3
The labelling on bags of garden compost indicates that the bags weigh 20 kg. Theweights of a random sample of 50 bags are summarised in the table below.
Weight in kg Frequency
14.6 – 14.8 1
14.8 – 18.0 0
18.0 – 18.5 5
18.5 – 20.0 6
20.0 – 20.2 22
20.2 – 20.4 15
20.4 – 21.0 1
Using the coding y = 10(weight in kg – 14), find an estimate for the mean and standard deviation of the weight of a bag of compost.
(6)
(Total 6 marks)
3.
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4
The following table summarises the times, t minutes to the nearest minute, recorded for agroup of students to complete an exam.
(a) Estimate the mean and standard deviation of these data.(5)
(b) Use linear interpolation to estimate the value of the median.(2)
(c) Show that the estimated value of the lower quartile is 18.6 to 3 significant figures.(1)
(d) Estimate the interquartile range of this distribution.(2)
(e) Without further calculations, explain the effect this would have on each of theestimates found in parts (a), (b), (c) and (d).
(3)
(Total 13 marks)
4.
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5
The person timing the exam made an error and each student actually took 5 minutes less than the times recorded above. The table below summarises the actual times.