jo teaches the violin. she wants to investigate the

Q1. Jo teaches the violin.

Half of her students take violins home to practise.

She wants to investigate the following hypothesis.

“Students who take violins home to practise score higher marks in violin exams.”

Use the data handling cycle to describe how Jo could carry out this investigation and test her hypothesis.

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t.hayes

Underline

Q2. A holiday park has three different areas to stay in. Each area has three different types of home.

The table shows the number of families staying in the holiday park during the summer of 2013.

The manager sends a questionnaire to 60 families to ask them about their holiday.

The sample of size 60 is stratified by type of home and area.

(a) How many families who stayed in a Luxury home in the Forest are sent a questionnaire?

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Answer ...................................................................... (2)

Area

Forest Fields Beach

Type of home

Economy 55 50 60

Super 35 20 15

Luxury 10 30 25

Total 100 100 100

(b) How many families who stayed in a Super home are sent a questionnaire?

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Answer ...................................................................... (2)

(Total 4 marks)

Q3. The manager of a company wants to survey his employees.

He decides to sample 20% of them, stratified by the type of job they do.

This table shows the number of employees.

Office staff Drivers Mechanics Total

12 24 4 40

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Fill in the table below to show how many of each group he should survey.

(Total 3 marks)

Office staff Drivers Mechanics

Q4. There are 36 men in a running club.

The pie chart shows information about their favourite races.

Men

There are 20 women in the running club.

Here is information about their favourite races.

The same proportion of women prefer the half marathon as men.

The same number of women prefer 5 km races as men.

Equal numbers of women prefer 10 km races and the marathon.

Use this information to draw a fully labelled pie chart to show the favourite races of the women.

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Women

(Total 4 marks)

Q5. The times taken by 100 students to travel to school are shown.

Time, t (minutes) Frequency

0 < t ≤ 10 36

10 < t ≤ 20 34

20 < t ≤ 30 18

30 < t ≤ 40 12

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(a) Draw a frequency diagram for the data.

(2)

(b) The school has 600 students.

Estimate how many students take more than 20 minutes to travel to school.

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Answer ...................................................................... (2)

(Total 4 marks)

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Q6. The times that 100 customers spent queuing in a post office were recorded. The cumulative frequency diagram shows the results.

(a) How many customers queued for more than 15 minutes?

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Answer ...................................................................... (1)

(b) Work out the median queuing time.

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Answer ........................................................ minutes (1)

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(c) A new serving window was opened in the post office. The times that 100 customers spent queuing were then recorded. The box plot shows the results.

Work out the inter-quartile range of these times.

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Answer ........................................................ minutes (2)

(d) Compare the queuing times before and after the new serving window was opened. Give two comparisons.

Comparison 1 ................................................................................................

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Comparison 2 .................................................................................................

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......................................................................................................................... (2)

(Total 6 marks)

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Q7. Cucumbers are grown in a greenhouse or in a garden. The box plots show data about their lengths, in centimetres.

Length (cm)

(a) Write down the median length of the cucumbers grown in the garden.

Answer ................................................................ cm (1)

(b) Give two comparisons between the lengths of cucumbers grown in the greenhouse and cucumbers grown in the garden.

Comparison 1 ................................................................................................

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Comparison 2 ................................................................................................

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........................................................................................................................ (3)

(Total 4 marks)

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Q8. The histogram represents the birth masses of 500 mice.

Birth mass (grams)

Work out the number of mice with birth masses below 10 grams.

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Answer ...................................................................... (Total 4 marks)

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Q9. A company has 800 workers. The table and histogram show the distribution of weekly wages.

Weekly wages, w (£) Frequency

0 < w ≤ 100

100 < w ≤ 200 150

200 < w ≤ 250 140

250 < w ≤ 300 120

300 < w ≤ 500

500 < w ≤ 600 20

Total 800

Complete both the table and the histogram. (Total 4 marks)

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Q10. Five whole numbers are written in order.

The mean and median of the five numbers are the same.

Work out the values of x and y.

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x = .................................. y = .................................. (Total 3 marks)

4 7 x y 11

Q11. The times that 100 customers spent queuing in a post office were recorded. The cumulative frequency diagram shows the results.

(a) How many customers queued for more than 15 minutes?

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Answer ...................................................................... (1)

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(b) Work out the median queuing time.

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Answer ........................................................ minutes (1)

(c) A new serving window was opened in the post office. The times that 100 customers spent queuing were then recorded. The box plot shows the results.

Work out the inter-quartile range of these times.

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Answer ........................................................ minutes (2)

(d) Compare the queuing times before and after the new serving window was opened. Give two comparisons.

Comparison 1 ................................................................................................

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Comparison 2 .................................................................................................

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......................................................................................................................... (2)

(Total 6 marks)

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Q12. Cucumbers are grown in a greenhouse or in a garden. The box plots show data about their lengths, in centimetres.

Length (cm)

(a) Write down the median length of the cucumbers grown in the garden.

Answer ................................................................ cm (1)

(b) Give two comparisons between the lengths of cucumbers grown in the greenhouse and cucumbers grown in the garden.

Comparison 1 ................................................................................................

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Comparison 2 ................................................................................................

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........................................................................................................................ (3)

(Total 4 marks)

Q13. A bag contains triangles and quadrilaterals in the ratio of the number of sides of each shape.

(a) Explain why the least number of shapes that could be in the bag is 7.

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......................................................................................................................... (1)

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(b) A shape is taken at random from the bag and replaced. Another shape is then taken from the bag.

Work out the probability that the two shapes taken from the bag are of the same type.

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Answer ...................................................................... (4)

(Total 5 marks)

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Q14. The relative frequencies of the number of absences in a school on 5 days are shown.

Day

There are 1600 students in the school.

How many more absences were there on Friday than on Monday?

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Answer ...................................................................... (Total 3 marks)

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M1. Reference to recording exam scores B1

Reference to recording exam scores for both groups B1

Record results in a way that allows a comparison (bar chart of totals, totals, average score for each group etc)

B1

Refers to comparing the results for their chosen method, eg higher total, bigger average and how this would confirm or deny the original hypothesis

Strand (iii) Must refer to third B1 for Q mark Q1dep

[4]

M2. (a) 60 ÷ 300 or or ÷ 5

oe, eg 20% M1

2 A1

(b) (35 + 20 + 15) ×

or 7 × their (a) but not if their (a) = 10

oe 7 + 4 + 3 M1

14 A1

[4]

M3.

B2 for two correct B2 for 1 correct and total of 8 The following for a maximum of 1 B1 for total of 8 B1 for 1 correct B1 for 12 ÷ 5 or 24 ÷ 5 or 4 ÷ 5 B1 for 2.4, 4.8 or 0.8 seen

[3]

Office staff Drivers Mechanics

2 5 1

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M4. Fully labelled diagram with angles Half-Marathon 90°

5K 126°

10K 72°

Marathon 72°

tolerance ± 2°for drawing B3 Angles correct but not labelled or wrongly labelled or angles correctly calculated and labelled but wrongly drawn. Part Marks to maximum of 3 B1 Half Marathon 90° and labelled B1 10K and Marathon equal angles or equal angles stated but drawn wrongly and labelled. B1 5K 126° and labelled The following only to be awarded if nothing drawn, or if working scores more than the diagram. B1 Working to show each angle for women = 18°. B1 all correct numbers of women in each category calculated, ie 5 for HM, 7 for 5K, 4 each for 5K and M.

B4 [4]

M5. (a) Histogram or frequency polygon with mid-points of bars and vertices of polygon at (5, 36), (15, 34), (25, 18) and (35, 12)

B1 one error Ignore lines before (5, 36) and after (35, 12) if polygon drawn

B2

(b) 6 × (18 + 12)

NB table can be seen if necessary.

oe × 600 M1

180 SC1 30% stated as answer SC1 for 420 as answer

A1 [4]

M6. (a) 20 B1

(b) 9 B1

(c) 11 and 3 seen Could be written on diagram

M1

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8 A1

(d) Comment on average and the implication, eg waiting times decreased after new window as median lower

ft their medians if valid conclusion reached B1

Comment on range or inter-quartile range and the implication, eg Spread of waiting times decreased after new window as range decreased or Not much effect on waiting times as IQR about the same

ft their values if a valid conclusion reached B1

[6]

M7. (a) 27 B1

(b) Comparison 1 on median eg length are about same as medians are similar. Greenhouse cucumbers are longer on average / as they have a higher median.

B1

Comparison 2 on interquartile range or range Greenhouse cucumbers are more consistent as range (or IQR) smaller. Garden cucumbers are more varied as range (or IQR) larger.

B1

Use of relevant values from both box plots for at least one comment. eg medians are 1cm different

Medians 28 and their 27

IQR 11 and 15

Range 26 and 33 Greenhouse cucumbers are more consistent with an IQR of 11 compared to 15

B1dep [3]

M8. Evidence that any bar area has been calculated eg applying a scale to side and multiplying by width. These should be multiples of 12, 16, 22, 23, 19 and 8 but as 23 and 19 can be read from graph, do not award for these values unless an area calculation seen

NB each little square is one mouse but if this is assumed and the total area is not shown to be 500 then only this M1 can be awarded.

M1

Total area calculated. Sum of above is 100. NB The bars cover 20 ‘big’ squares, so if this is stated this is M1, A1

A1

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Area scaled to 500 or a calculation done such as 12 × 500 ÷ 100 Scale of 25, 50 for ‘big’ squares as fd.

M1

60 This must come from valid working, so answer of 60 alone or 60 from, say, 3 × 20 is M1. ft their first bar total × 500 ÷ their total and rounded or truncated to an integer.

A1ft

Alternative Method

20 ‘big’ squares stated as area of all bars M1

500 ÷ 20 (= 25) A1

Their 25 × 2.4 M1

60 A1ft

[4]

M9. 90 B1

280 ft 370 − their 90

B1ft

Bar from 250 to 300 with a height of 2.4 B1

Bar from 300 to 500 with a height of 1.4 ft their 280 ÷ 200

B1ft [4]

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M10. 8 and 10

B2 for any whole number combination that satisfies the median equal to the mean. There are an infinite number. Common ones are (1, 12), (2, 11), (3, 10), (4, 9), (5, 8), (2, 6), (6, 7), (9, 14), (10, 18), (11, 22) (11 + n, 22 + 4n), (15, 18), (16, 17), (any pair greater than 11 that total 33). B1 for any decimal combination that satisfies the median equal to the mean. There are an infinite number. Common ones are (7.5, 8), (8.5,12), (8.5 + n, 12 + 4n).

B3

Alternative Method 1

22 + x + y = 5x oe M1

4x − y = 22 oe M1

8 and 10 A1

Alternative Method 2

Chooses values for x and y (which may be the same) where both are between 7 and 11 inclusive and calculates mean correctly or compares total to 5x. e.g. 8 and 9 chosen, Mean = 39 ÷ 5 = 7.8 or total = 39 ≠ 40 NB an attempt at another pair of values implies rejection of first pair

M1

Chooses two further values for x and y where both are between 7 and 11 inclusive and calculates mean correctly or compares total to 5x. e.g. 9 and 10 chosen, Mean = 41 ÷ 5 = 8.2 or total = 41 > 40

M1

8 and 10 A1

[3]

M11. (a) 20 B1

(b) 9 B1

(c) 11 and 3 seen Could be written on diagram

M1

8 A1

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(d) Comment on average and the implication, eg waiting times decreased after new window as median lower

ft their medians if valid conclusion reached B1

Comment on range or inter-quartile range and the implication, eg Spread of waiting times decreased after new window as range decreased or Not much effect on waiting times as IQR about the same

ft their values if a valid conclusion reached B1

[6]

M12. (a) 27 B1

(b) Comparison 1 on median eg length are about same as medians are similar. Greenhouse cucumbers are longer on average / as they have a higher median.

B1

Comparison 2 on interquartile range or range Greenhouse cucumbers are more consistent as range (or IQR) smaller. Garden cucumbers are more varied as range (or IQR) larger.

B1

Use of relevant values from both box plots for at least one comment. eg medians are 1cm different

Medians 28 and their 27

IQR 11 and 15

Range 26 and 33 Greenhouse cucumbers are more consistent with an IQR of 11 compared to 15

B1dep [3]

M13. (a) 3 + 4 = 7 or 3 : 4 = total 7

3 and 4 do not have any common factors (apart from 1) oe

B1

(b) and seen or 2 equivalent fractions

M1

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or or or Maybe on tree diagram with appropriate branches shown and probability calculation shown for at least one pair of branches

M1dep

1 − 2 × M1dep

ft if without replacement calculated

SC2 from A1ft

[5]

M14. 0.05 − 0.03 (= 0.02)

0.05 × 1600 (= 80) or 0.03 × 1600 (= 48) M1

Their ‘0.02’ × 1600 Their 80 − their 48

M1dep

32 SC1 Digits 32 eg 0.32, 320 etc imply method SC2 Use of 0.015 for Monday instead of 0.03 giving an answer of 56

A1 [3]

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jo teaches the violin. she wants to investigate the

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