Pre-course task for 2015 entry
Welcome to AS Statistics!
A Level Statistics is a great choice for study at New College – it goes well with so many of our other
subjects, from Geography and Psychology, to Science, Business and even AS Maths and AS Use
of Maths!
This is a demanding course. You may be taking AS Statistics because you studied and enjoyed
GCSE Statistics, but as long as you studied GCSE Maths at higher tier you should be fully
prepared for the challenges that lie ahead. This task contains some of those higher tier questions
for you to complete so that you are able to hit the floor running when you arrive in September.
Many of the topics you will study in the first term will be familiar to you already, such as averages,
range and interquartile range, probability and scatter diagrams and the concept of correlation. But
we will quickly move on to new material like the Binomial distribution, Normal distribution and
equations of regression lines. Completing this task will help to ensure that are able to keep up with
the course and move on to the new topics early on.
You should have this task completed by Monday 29th June which is our Welcome Day and
you should hand it in to your subject workshop leader on this day. You will shortly be
receiving an invite to this event. Please ensure your name is written on the top of every
page of work you produce. This work comprises an element of the assessment used during
induction.
The course has two sides to it. On the one hand, we will need to consider how our results relate to
real life, trying to understand results in the context of a problem. On the other hand we actually
have to be able to calculate results in the first place! A large part of this will be using a graphical
calculator. We use CASIO fx-9750GII, and purchase of this calculator is compulsory for enrolment
on the course. This can be purchased from us for approximately £60 when you enrol.
Wishing you the best of luck for your GCSE results and looking forward to meeting you in
September.
Martin Farran
Course Leader, AS Statistics
What will I study in AS Statistics?
You will study three modules, Statistics 1, Statistics 2 and Statistics 3. Each of these is assessed
by 90 minute exam in the summer, and require use of a graphical calculator.
For more information go to http://www.aqa.org.uk/subjects/mathematics/a-level/statistics-6380
Statistics 1 Content
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Averages and measures of spread.
Probability, mutually exclusive events, and set notation.
The Binomial distribution
The Normal distribution
Sampling
Confidence intervals
Correlation and regression
Statistics 2 Content
 Time Series and moving averages
 Sampling
 Variance and Expectation for probability distributions.
 The Poisson distribution
 Pie charts, line diagrams, box and whisker plots, and cumulative frequency diagrams.
 Hypothesis testing.
Statistics 3 Content
 Contingency tables
 The Wilcoxon signed-rank test.
 The Mann-Whitney U test.
 The Kruskal-Wallis test.
 Correlation and Spearman’s rank correlation coefficient.
Questions
Q1.
The scatter graph shows information about the height and the arm length of each of 8 students in Year 11
(a) What type of correlation does this scatter graph show?
...........................................................
(1)
A different student in Year 11 has a height of 148 cm.
(b) Estimate the arm length of this student.
...........................................................cm
(2)
(Total for Question is 3 marks)
Q2.
The table gives some information about the birds Paula sees in her garden one day.
Bird
Frequency
Magpie
Thrush
Starling
Sparrow
15
10
20
27
Complete the accurate pie chart.
(Total for Question is 3 marks)
Q3.
There are only red counters, blue counters, white counters and black counters in a bag.
The table shows the probability that a counter taken at random from the bag will be red or blue.
Colour
red
blue
Probability
0.2
0.5
white
black
The number of white counters in the bag is the same as the number of black counters in the bag.
Tania takes at random a counter from the bag.
(a) Work out the probability that Tania takes a white counter.
..............................................................................................................................................
(2)
There are 240 counters in the bag.
(b) Work out the number of red counters in the bag.
..............................................................................................................................................
(2)
(Total for Question is 4 marks)
Q4.
The probability that a biased dice will land on a five is 0.3
Megan is going to roll the dice 400 times.
Work out an estimate for the number of times the dice will land on a five.
..............................................................................................................................................
(Total for Question is 2 marks)
Q5.
The scatter graph shows some information about ten pine cones from the same tree.
It shows the length and the width of each pine cone.
(a) Describe the relationship between the length and the width of a pine cone.
.............................................................................................................................................
.............................................................................................................................................
(1)
Another pine cone from this tree has a length of 8.4 cm.
(b) Estimate the width of this pine cone.
...........................................................cm
(2)
(Total for question = 3 marks)
Q6.
Wendy goes to a fun fair.
She has one go at Hoopla.
She has one go on the Coconut shy.
The probability that she wins at Hoopla is 0.4
The probability that she wins on the Coconut shy is 0.3
(a) Complete the probability tree diagram.
(2)
(b) Work out the probability that Wendy wins at Hoopla and also wins on the Coconut shy.
..............................................................................................................................................
(2)
(Total for Question is 4 marks)
Q7.
25 students in class A did a science exam.
30 students in class B did the same science exam.
The mean mark for the 25 students in class A is 67.8
The mean mark for all the 55 students is 72.0
Work out the mean mark for the students in class B.
...........................................................
(Total for Question is 3 marks)
Q8.
In a supermarket, the probability that John buys fruit is 0.7
In the same supermarket, the probability that John independently buys vegetables is 0.4
Work out the probability that John buys fruit or buys vegetables or buys both.
...........................................................
(Total for Question is 3 marks)
Q9.
Harry grows tomatoes.
This year he put his tomato plants into two groups, group A and group B.
Harry gave fertiliser to the tomato plants in group A.
He did not give fertiliser to the tomato plants in group B.
Harry weighed 60 tomatoes from group A.
The cumulative frequency graph shows some information about these weights.
(a) Use the graph to find an estimate for the median weight.
......................g
(1)
The 60 tomatoes from group A
had a minimum weight of 153 grams
and a maximum weight of 186 grams.
(b) Use this information and the cumulative frequency graph to draw a box plot for the 60 tomatoes from
group A.
(3)
Harry did not give fertiliser to the tomato plants in group B.
Harry weighed 60 tomatoes from group B.
He drew this box plot for his results.
(c) Compare the distribution of the weights of the tomatoes from group A with the distribution of the
weights of the tomatoes from group B.
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
(2)
(Total for Question is 6 marks)
Q10.
(a) Explain what is meant by a stratified sample.
.............................................................................................................................................
.............................................................................................................................................
(1)
The table shows information about the ages of the people living in a village.
Mrs Parrish carries out a survey of these people.
She uses a sample size of 50 people stratified by age group.
(b) Work out the number of people over 60 years of age in the sample.
...........................................................
(2)
(Total for Question is 3 marks)
Q11.
Jane has a packet of seeds.
The probability that a seed will grow is 0.75
(a) What is the probability that a seed will not grow?
...........................................................
(1)
Jane plants 200 of these seeds.
(b) Estimate the number of the seeds that will grow.
...........................................................
(2)
(Total for Question is 3 marks)
Q12.
Bob asked each of 40 friends how many minutes they took to get to work.
The table shows some information about his results.
Time taken (m minutes)
Frequency
0 < m ≤ 10
10 < m ≤ 20
20 < m ≤ 30
30 < m ≤ 40
40 < m ≤ 50
3
8
11
9
9
Work out an estimate for the mean time taken.
. . . . . . . . . . . . . . . . . . . . . . minutes
(Total for Question is 4 marks)
Q13.
Lorna carries out a survey about the number of times customers go to a shop.
She asks at random 100 customers how many times they went to the shop last month.
The table shows Lorna's results.
One of the 100 customers is chosen at random.
(a) What is the probability that this customer went to the shop 5 or more times?
...........................................................
(2)
Last month the shop had a total of 1500 customers.
(b) Work out an estimate for the number of customers who went to the shop exactly 2 times last month.
...........................................................
(2)
The owner of a different shop is carrying out a survey on the ages of his customers.
He records the ages of the first 10 customers in his shop after 9 am one morning.
(c) This may not be a suitable sample.
Give two reasons why.
1
.............................................................................................................................................
.............................................................................................................................................
2
.............................................................................................................................................
.............................................................................................................................................
(2)
(Total for Question is 6 marks)
Q14.
Here are seven tiles.
Jim takes at random a tile.
He does not replace the tile.
Jim then takes at random a second tile.
(a) Calculate the probability that both the tiles Jim takes have the number 1 on them.
..............................................................................................................................................
(2)
(b) Calculate the probability that the number on the second tile Jim takes is greater than the number on the
first tile he takes.
..............................................................................................................................................
(3)
(Total for Question is 5 marks)