The Robert Smyth School Module 1
Mathematics Faculty (2b) Analysing & Processing
Finding the mean, median, mode + range
1. (a) The table shows some information about the cars for sale at a garage.
Make / Colour / Price (£) / MileageRover / Silver / 7 000 / 21 000
Ford / Black / 2 999 / 63 000
Honda / Green / 1 500 / 124 000
Ford / Black / 950 / 89 000
BMW / White / 11 000 / 25 000
Vauxhall / Red / 2 750 / 55 000
Citroen / Black / 895 / 94 000
(i) Which colour of car is the mode?
Answer ......
(1)
(ii) How many cars are on sale for less than £2 000?
Answer ......
(1)
(iii) Calculate the range of the mileages of the seven cars.
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Answer ...... miles
(1)
(Total 3 marks)
2. A club sells raffle tickets for £1 each.
The winning prize is £100.
20 people bought 1 ticket each.
80 people bought 2 tickets each.
40 people bought 3 tickets each.
50 people bought 4 tickets each.
(a) Calculate the number of tickets that were sold altogether.
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Answer ......
(2)
(b) Calculate the mean profit made per ticket on this raffle.
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Answer £ ......
(2)
(Total 4 marks)
3. The Quickpass driving school records the number of lessons that each person had before passing their driving test.
The results for seven men are shown.
10 17 15 10 12 8 19
(a) Work out the range of these numbers.
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Answer ………………………………………
(1)
(b) Calculate the mean of these numbers.
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Answer ………………………………………
(3)
(c) Find the median.
Answer ......
(1)
(d) The number of driving lessons taken by a sample of women is summarised in the table.
Women
Range / 14Mean / 9
Write down two comparisons between the number of driving lessons taken by the men and the women.
Comparison 1 ......
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Comparison 2 ……………………………………………………………………….
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(2)
(Total 7 marks)
Finding the mean from frequency tables
1. A charity sells raffle tickets for 50p each.
The winning prize is £100.
50 people bought 1 ticket each.
80 people bought 2 tickets each.
70 people bought 3 tickets each.
95 people bought 4 tickets each.
40 people bought 5 tickets each.
Calculate how much profit the charity made on this raffle.
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Answer £ …………………………………….
(Total 4 marks)
2. A telephone company collected data about the number of telephones in each of 60 households. The table shows the results.
Number oftelephones / Number of
households
0 / 2
1 / 15
2 / 12
3 / 10
4 / 8
5 / 7
6 / 5
7 / 0
8 / 1
(a) Calculate the total number of telephones in these 60 households.
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Answer ......
(2)
(b) Calculate the mean number of telephones per household.
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Answer ......
(2)
(Total 4 marks)
3. Phil counts the number of people in 50 cars that enter a car park.
His results are shown in the table.
Number of people / Frequency1 / 25
2 / 17
3 / 6
4 / 2
more than 4 / 0
Calculate the mean number of people per car.
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Answer ......
(Total 3 marks)
4. Chloe records the number of goals scored by her favourite football team in each of 40 matches.
Number of goals / Frequency0 / 7
1 / 15
2 / 13
3 / 2
4 / 2
5 / 1
(a) Write down the mode of the number of goals scored.
Answer ......
(1)
(b) Calculate the mean number of goals scored per match.
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Answer ......
(3)
(Total 4 marks)
5. Chloe records the number of goals scored by her favourite football team in each of 40 matches.
Number of goals / Frequency0 / 7
1 / 15
2 / 13
3 / 2
4 / 2
5 / 1
Chloe’s father watched one of these matches on TV.
What is the probability that the team scored at least one goal in that match?
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Answer ......
(2)
(Total 2 marks)
6. (a) The National Curriculum levels in Mathematics for 30 students in year 9 were recorded.
3 / 0
4 / 4
5 / 4
6 / 9
7 / 8
8 / 5
Calculate the mean level.
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Answer......
(3)
(b) The 30 students study both French and Spanish.
Their National Curriculum levels in these subjects are shown in the two-way table.
1 / 2 / 3 / 4 / 5 / 6
Level / 1 / 0 / 0 / 0 / 0 / 0 / 0
in / 2 / 1 / 0 / 0 / 0 / 0 / 0
French / 3 / 2 / 1 / 1 / 0 / 0 / 0
4 / 0 / 3 / 4 / 1 / 0 / 0
5 / 0 / 1 / 2 / 3 / 2 / 0
6 / 0 / 0 / 3 / 3 / 2 / 1
(i) What is the median level for French?
Show clearly how you obtained your answer.
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Answer......
(2)
(ii) The teacher claims that the students are better at French than at Spanish. How can you tell from the table that this is true?
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(1)
(Total 6 marks)
Finding an Estimate of the Mean
1. A police officer records the speeds of 60 cars on a dual carriageway.
Speed (mph) / Frequency / Midpoint40 to less than 50 / 9
50 to less than 60 / 27
60 to less than 70 / 21
70 to less than 80 / 3
(a) Write down the modal class.
Answer ...... mph
(1)
(b) Use the class midpoints to calculate an estimate of the mean speed of these cars.
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Answer ...... mph
(3)
(Total 4 marks)
2. Jane records the times taken by 30 pupils to complete a number puzzle.
Time, t (minutes) / Number of pupils2 < t £ 4 / 3
4 < t £ 6 / 6
6 < t £ 8 / 7
8 < t £ 10 / 8
10 < t £ 12 / 5
12 < t £ 14 / 1
Calculate an estimate of the mean time taken to complete the puzzle.
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Answer ...... minutes
(4)
3. The table shows the age, in years, of workers in a factory.
Age, x (years) / Number of workers15 £ x < 20 / 4
20 £ x < 25 / 10
25 £ x < 30 / 6
30 £ x < 40 / 22
40 £ x < 60 / 8
Calculate an estimate of the mean age of these workers.
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Answer ...... years
(Total 4 marks)
The Robert Smyth School 8