1.
The pie chart shows information about the numbers of officers in the Royal Navy, Army and
Air Force.
Officers in the Royal Navy, Army and Air Force
Royal Navy
Army
Air Force
Total: 30 000 officers
The pie chart is misleading.
(a)
Write down one reason why.
.....................................................................................................................................
(1)
A new pie chart is to be drawn which is not misleading.
The number of officers in the Royal Navy is 7000
(b)
Calculate the angle needed for the Royal Navy.
.......................... °
(2)
(Total 3 marks)
2.
The pie chart gives information about land use in the U.K.
Land use in the U.K.
Inland waterways
Urban land
Forest
Rough grazing
Other forms of
agriculture
Crops
(Source: www.sustainable-development.gov.uk)
Describe two features of the diagram that can be misleading.
1 ............................................................................................................................................
...............................................................................................................................................
2 ............................................................................................................................................
...............................................................................................................................................
(Total 2 marks)
3.
The comparative pie charts show some information about the players at Seaton squash club in
1980 and in 1990.
The three types of players at Seaton squash club are Senior male, Senior female and Junior.
1990
Senior male
1980
Senior female
Junior
(Data source: Seaton squash club)
(a)
What has happened to the number of Senior male players at Seaton squash club between
1980 and 1990? Give a reason for your answer.
.....................................................................................................................................
.....................................................................................................................................
(2)
The table shows the numbers of players in 2005.
Number of players
Senior male
197
Senior female
108
Junior
81
A stratified sample of 40 players was taken from the 386 players of the club.
(b)
Explain why a stratified sample was taken.
.....................................................................................................................................
.....................................................................................................................................
(1)
(c)
Work out the number of Junior players who were selected for the stratified sample.
.................................
(1)
(Total 4 marks)
4.
A farmer has two farms.
On one farm he has battery hens, on the other farm he has the same number of free-range hens.
One Saturday the sizes of the eggs collected from the two farms were as follows:
Large
Medium
Small
Free-range hens
125
210
105
Battery hens
75
210
125
Total number
of eggs
Totals
(a)
Complete the two-way table.
(2)
An egg from those collected on the Saturday is chosen at random.
(b)
Write down the probability that the egg chosen is
(i)
large,
............................
(ii)
from a free-range hen and medium.
............................
(2)
(c)
Compare and contrast the numbers of the different sizes of eggs laid by the free-range
hens and the battery hens on these farms.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 6 marks)
5.
The comparative pie charts give information about the numbers of people living in six
continents of the world.
(a)
What has happened to the total number of people living in the world in 1980 compared to
2007? Explain how you can tell this from the pie charts.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(b)
Write down the name of the continent with the greatest increase in population.
............................................................
(1)
(c)
Describe how the total number of people living in Oceania has changed in 1980
compared to 2007. Explain your answer.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 5 marks)
6.
This table below is part of a larger table that shows the percentages of male and female pupils
achieving GCSEs in the United Kingdom in 2001/ 2002.
Examination Achievements 2001/ 2002
Males
United Kingdom
Females
United Kingdom
Pupils in the last year of compulsory education
Percentage achieving GCSE
5 or more 1-4 grades Grades D-G No graded
Total
grades
A*-C
only
GCSEs
(=100%)
A*-C
(thousands)
45.7
24.6
23.1
6.5
372.1
56.5
23.6
15.5
4.4
357.6
Source: Department of Education and Skills
(a)
The percentages for the male pupils do not add up to 100%. Explain why.
......................................................................................................................................
......................................................................................................................................
(1)
(b)
Using the following grid, draw composite bar charts to show the data given in the table
above.
100%
90%
80%
70%
60%
50%
40%
30%
20%
Key
5 or more A* –C
grades
1 - 4 A* –C
grades
Grades D - G
only
No graded
GCSEs
10%
0%
(3)
(Total 4 marks)
7.
There has been research into the survival of Red Squirrels.
A large number of adult Red Squirrels and a large number of adult Grey Squirrels were
weighed.
The summary statistics of body weights are shown in the table.
Weight in
grams
Minimum
weight (g)
Lower
quartile (g)
Median
weight (g)
Upper
quartile (g)
Maximum
weight (g)
Red
Squirrel
240
260
300
340
360
Grey
Squirrel
300
450
500
570
620
A box plot has been drawn on the grid to show the distribution of the weights of Red Squirrels.
Distributions of the weights of squirrels
Red
Squirrel
Grey
Squirrel
200
300
400
500
600
700
Weight (g)
(Source: Wildlife Trust’s Squirrel Survey)
(a)
On the grid, draw a box plot to show the distribution of the weights of Grey Squirrels.
(3)
(b)
Describe the skewness of each of the distributions.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(c)
Compare the distributions of the weights of the Red Squirrels and the weights of the Grey
Squirrels.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
Some Grey Squirrels have a lot of red fur.
Some Red Squirrels have some grey fur.
This means that it is not always possible to tell if a squirrel is red or grey by looking at the
colour of its fur.
There are Red Squirrels and Grey Squirrels in a wood.
(d)
How could you use the box plots to help you find out whether a certain squirrel is a Red
Squirrel or a Grey Squirrel?
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 9 marks)
8.
Some people were asked which one of three newspapers they prefer.
The results, by gender, are shown in the table.
Males
Females
The Sun
45
34
The Daily Telegraph
11
10
The Times
10
7
Total
Total
(a)
Complete the table.
(2)
(b)
Write down the two variables used in the table.
........................................................
........................................................
(2)
One of these people is picked at random.
(c)
(i)
Write down the probability that this person is a female who prefers The Times.
.........................
(1)
(ii)
Given that the person picked is a male, write down the probability that he prefers
The Sun.
.........................
(2)
(Total 7 marks)
The weight, in kg, of 50 people in a club was recorded. The results are summarised in the
cumulative frequency diagram.
Weight of people in a club
50
Cumulative frequency
9.
40
30
20
10
0
55
60
65
70
75
80
Weight (kg)
85
90
95
(a)
Using the cumulative frequency diagram, find an estimate for
(i)
the median,
…………………………………… kg
(ii) the inter-quartile range.
………………………………….... kg
(3)
(b)
Write down the percentage of the weights represented by the inter-quartile range.
...........………………%
(1)
The lowest weight recorded was 50 kg and the heaviest was 90 kg.
(c)
Draw a box plot for this data.
(3)
(d)
Describe the shape of this distribution.
...............................................................................................................................................
(1)
(Total 8 marks)
10.
Source: www.statistics.gov.uk/census2001/pyramids/pages/uk.asp
The diagram shows information about the population of Camden in 2001.
(a)
What is the name of this type of diagram?
...............................................................................................................................................
(1)
Use the diagram to answer the following questions about the population of Camden.
(b)
Write down the age group that has the largest population.
............................................
(1)
(c)
Work out an estimate for the percentage of the female population under 20 years old.
............................................
(1)
The following diagram shows information about the population of Northern Ireland in 2001.
Source: www.statistics.gov.uk/census2001/pyramids/pages/uk.asp
(d)
Give one similarity and one difference between the population of Camden and the
population of Northern Ireland.
Similarity ..............................................................................................................................
...............................................................................................................................................
Difference .............................................................................................................................
...............................................................................................................................................
(2)
(Total 5 marks)
12.
The box and whisker diagram gives information about the room occupancy rates (%) of 15
resorts in Yorkshire during 1999.
(Source: Yorkshire Tourist Board)
(a)
Write down the median room occupancy rate.
.............................................%
(1)
(b)
Work out the interquartile range.
.............................................%
(2)
(c)
A normal distribution is suggested as a model for the room occupancy rates in Yorkshire
in 1999. Give a reason which supports this choice.
.....................................................................................................................................
.....................................................................................................................................
(1)
During 2006 the room occupancy rates (%) for the same 15 resorts were
50 51 61 65 52 54 55 66 55 55 69 55 69 55
56
(Source: Yorkshire Tourist Board)
(d)
For the 2006 room occupancy rates,
(i)
find the median,
.............................................%
(2)
(ii)
find the interquartile range,
.............................................%
(3)
(iii)
describe the skew.
...........................................................................................................................
(1)
(e)
Compare the distribution of the 1999 room occupancy rates with the distribution of the
2006 room occupancy rates.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 12 marks)
13.
A holiday company recorded the ages, in years, of the people on each of two tours.
The ages of the people on tour A are summarised in this box plot.
30
40
50
60
70
80
90
Age (years)
(Data source: Blue Lagoon)
(a)
Describe the skewness of the distribution of the ages of the people on tour A.
................................
(1)
(b)
What percentage of these ages lie between the upper and lower quartiles?
................................
(1)
Here are the ages of the people on tour B.
(c)
32
33
35
39
43
44
44
47
48
48
50
52
54
55
55
57
58
60
65
68
70
86
51
For the ages of the people on tour B, find
(i)
the median,
................................
(ii)
the lower quartile,
................................
(iii)
the upper quartile.
................................
(3)
(d)
Show that 86 is an outlier for the ages of the people on tour B.
(3)
There are no other outliers.
(e)
On the grid, draw a box plot to show the distribution of the ages of the people on tour B.
Tour A
Tour B
30
40
50
60
70
80
90
Age (years)
(3)
(f)
Compare the distributions of the ages of the people on the two tours.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 13 marks)
15.
In a study on identical twins, the intelligence quotient (IQ) of 10 sets of twins was tested, and
whether the twin was the first- or the second-born was recorded.
The results for the second-born twins are shown on the stem and leaf diagram below.
Second-born twins’ IQ
(a)
8
7
9
9
3
4
10
1
3
11
3
12
6
6
7
Key
8  7 = 87
Find the median IQ of the second-born twins.
............................
(1)
(b) Find the lower and upper quartiles of the IQs of second-born twins.
Lower quartile ............................
Upper quartile ............................
(2)
(c)
Show that 126 is not an outlier for the second-born twins’ IQs.
(3)
The IQs of the first-born twins are shown as a box plot on the grid below.
(d)
On the same grid draw a box plot for the IQs of the second-born twins.
Comparative box plots
First–born
Second–born
80
90
100
110
120
130
140
IQ
(3)
(e)
Compare the two distributions.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(f)
Suggest one way in which the study could be improved.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(1)
(Total 12 marks)
16.
The table shows how the average price of houses bought by first-time buyers changed over a
period of five years. It also shows some of the chain base index numbers for the average prices.
The average prices are given to the nearest £1000.
Year
2001
2002
2003
2004
2005
Price (£1000s)
68
85
99
121
129
Chain base index number
123
125
116
(Data source: Nationwide Database of House Prices)
(a)
Calculate, to the nearest whole number, the chain base index numbers for the years 2004
and 2005, and enter them in the table.
(2)
(b)
For the years 2001 to 2005 write down the largest annual percentage increase.
............................%
(1)
(c)
Calculate the geometric mean of the chain base index numbers for these five years.
............................
(2)
(d)
What can you infer from your answer to (c)?
.....................................................................................................................................
.....................................................................................................................................
(1)
(e)
Discuss the trend of the chain base index numbers.
.....................................................................................................................................
.....................................................................................................................................
(1)
(Total 7 marks)
17.
Zenith Engineering makes stainless steel.
The raw materials for making stainless steel are steel, chromium and nickel.
A stainless steel is made with 74% steel, 18% chromium and 8% nickel.
The table shows the price, in pounds per ton, for chromium and nickel in the years 2000 and
2003.
Metal prices
Year
(a)
2000
2003
Chromium (£/ton)
41 500
43 575
Nickel (£/ton)
8 000
8 240
Taking 2000 as the base year, calculate the index numbers for the price of chromium and
nickel in 2003.
Metal
Index 2000
Index 2003
Steel
100
102
Chromium
100
Nickel
100
Chromium ……….
Nickel ……….
(3)
The index number for the price of steel in 2003 was 102.
Zenith Engineering wants to find out the weighted index number for the price of the raw
materials for stainless steel.
(b)
Calculate this number.
...........................
(3)
(c)
Write down the percentage by which the price of raw materials for stainless steel went up
between 2000 and 2003.
...........................
(1)
(Total 7 marks)
14.
Working days were lost in the Manufacturing Industries and in the Public Administration and
Defence Industry between August 2000 and May 2001 as a result of strikes.
The table shows the number of working days, in thousands, lost each month.
Year
2000
Month
2001
Aug
Sep
Oct
Nov
Dec
Jan
Feb Mar Apr May
Manufacturing
14
4
2
6
8
2
6
9
2
4
Public Administration
and Defence
14
13
0
15
5
6
5
7
2
0
(Data source: Government Statistics)
The mean value of the number of working days lost each month in the Manufacturing Industries
is 5.7 thousand.
The standard deviation of the number of working days lost each month in the Public
Administration and Defence Industry is 5.3 thousand, to one decimal place.
(a)
(i)
Calculate the mean value of the number of working days lost each month in the
Public Administration and Defence Industry.
Mean for Public Administration and Defence ..................... thousands
(ii)
Calculate the standard deviation of the number of working days lost each month in
the Manufacturing Industries. Give your answer to one decimal place.
Standard deviation for Manufacturing ..................... thousands
(3)
You may assume that, between August 2000 and May 2001, there were approximately the same
number of people employed in the Manufacturing Industries as there were employed in the
Public Administration and Defence Industry.
(b)
Using the given summary statistics and your answers to part (a), compare the numbers of
working days lost each month due to strikes in the two industries between August 2000
and May 2001.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 5 marks)