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20 questions at your level
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Level 1
Level 2
Level 3
Level 4
Level 5
Scatter graphs & correlation
10 questions
Lesson
Not started
Mark as done
The scatter graph shows the hours students revised and their test scores.
2
4
6
8
10
20
30
40
50
60
70
80
Hours revised
Test score
Describe the type of correlation shown.
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Level 1
1 mark
Start
→
Mark as done
A scatter graph of the age of a car against its value shows that as age increases, value decreases. What type of correlation is this?
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Level 1
1 mark
Start
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Mark as done
For each of
10
10
10
days in November, a café recorded the midday temperature, in °C, and the number of hot chocolates it sold that day. The scatter graph shows this information.
5
10
15
20
10
20
30
40
50
60
Midday temperature (°C)
Hot chocolates sold
(a)
Write down what one point on the scatter graph represents.
(b)
On how many of these days did the café sell more than
40
40
40
hot chocolates?
(c)
Describe the correlation shown by the scatter graph.
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Level 2
4 marks
Start
→
Mark as done
Twelve members of an athletics club each ran
100
100
100
m and each did a long jump. The scatter graph shows each member's
100
100
100
m time, in seconds, and the length of their long jump, in metres.
12
12.5
13
13.5
14
14.5
15
15.5
16
3
3.5
4
4.5
5
100 m time (s)
Long jump (m)
(a)
Describe the correlation shown by the scatter graph.
(b)
Sam looks at the scatter graph and says: "This proves that a person's sprinting ability affects how far they can long jump."
Explain why the scatter graph does
not
show this.
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Level 3
4 marks
Start
→
Mark as done
Ten pupils each sat a maths test and a physics test. Both tests were marked out of
100
100
100
.
Ellie plotted their marks and then joined the points with a ruler, as shown. She says this is her line of best fit.
30
40
50
60
70
80
90
30
40
50
60
70
80
90
Maths mark
Physics mark
(a)
Explain why what Ellie has drawn is not a line of best fit.
(b)
Describe the correlation shown by the ten points.
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Level 3
4 marks
Start
→
Mark as done
Diagram 1
shows, for each of
12
12
12
days, the number of hours of daylight and the number of units of electricity used by a school.
8
9
10
11
12
13
14
350
400
450
500
550
600
650
Hours of daylight
Electricity used (units)
Diagram 2
shows, for each of
12
12
12
Year 11 pupils, the time taken to travel to school and the mark scored in a maths test.
5
10
15
20
25
30
35
20
25
30
35
40
45
50
55
60
Travel time (minutes)
Maths mark
(a)
Describe the correlation shown in Diagram 1.
(b)
Describe the correlation shown in Diagram 2.
(c)
Explain what your answer to part
(b)
tells you about travel time and maths marks for these pupils.
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Level 3
4 marks
Start
→
Mark as done
A researcher recorded, for each of
12
12
12
secondary schools, the number of computers the school owns and the total number of GCSE passes gained by its pupils last summer. The scatter graph shows the results.
20
40
60
80
100
120
140
160
100
200
300
400
500
600
700
Number of computers
Number of GCSE passes
A local newspaper printed the headline:
"Buying more computers raises GCSE results."
Explain why the researcher's data does not support this headline. You must refer to the scatter graph in your answer.
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Level 4
3 marks
Start
→
Mark as done
A café recorded, for each of
8
8
8
weeks, the amount it spent on local advertising and the number of customers it served that week.
Ben has drawn the straight line shown on the scatter graph and says it is his line of best fit.
20
40
60
80
100
120
140
160
100
200
300
400
500
Spent on advertising (£)
Number of customers
(a)
Give
two
reasons why Ben's line is not a good line of best fit.
(b)
Ben then says: "The correlation between the amount spent on advertising and the number of customers must be weak."
Explain why Ben is wrong.
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Level 4
3 marks
Start
→
Mark as done
In an experiment,
9
9
9
identical bean plants were each given a different mass of fertiliser. The table shows the mass of fertiliser, in grams, and the height of each plant, in centimetres, after four weeks.
Fertiliser
(g)
Height after 4 weeks (cm)
2
18
4
24
6
27
8
33
10
38
12
25
14
47
16
51
18
57
The scatter graph shows the same information.
5
10
15
20
10
20
30
40
50
60
Fertiliser (g)
Height (cm)
(a)
One of the plants is an outlier. Write down the mass of fertiliser that this plant was given.
(b)
Give a possible reason why this plant does not fit the pattern.
(c)
Describe the correlation shown by the other eight plants.
(d)
Draw a line of best fit for the other eight plants on the scatter graph.
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Level 4
5 marks
Start
→
Mark as done
A supermarket recorded, for each of
12
12
12
weeks last winter, the number of woolly hats it sold and the number of tins of soup it sold. The scatter graph shows this information.
100
150
200
250
300
600
700
800
900
1000
1100
1200
1300
Woolly hats sold
Tins of soup sold
(a)
Describe the correlation shown by the scatter graph.
(b)
The manager says: "This shows that selling woolly hats affects how much soup our customers buy."
Explain why the scatter graph does not support what the manager says.
(c)
The manager wants a line of best fit to be drawn, and insists that it must pass through
(
0
,
0
)
(0,\ 0)
(
0
,
0
)
.
Explain why drawing the line through
(
0
,
0
)
(0,\ 0)
(
0
,
0
)
would not be sensible here.
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Level 5
5 marks
Start
→
Predicting from a line of best fit
10 questions
Lesson
Not started
Mark as done
The scatter graph shows the hours students revised and their test scores, with a line of best fit.
2
4
6
8
10
20
30
40
50
60
70
80
Hours revised
Test score
Use the line of best fit to estimate the score of a student who revised for
4.5
4.5
4.5
hours.
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Level 1
1 mark
Start
→
Mark as done
The scatter graph shows the hours students revised and their test scores, with a line of best fit.
2
4
6
8
10
20
30
40
50
60
70
80
Hours revised
Test score
Explain why the line should
not
be used to estimate the score of a student who revised for
20
20
20
hours.
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Level 1
1 mark
Start
→
Mark as done
On 14 days a beach café recorded the number of hours of sunshine and the number of customers it served. The scatter graph shows the results, with a line of best fit drawn.
1
2
3
4
5
6
7
8
50
100
150
200
hours of sunshine
customers
(a)
Use the line of best fit to estimate the number of customers on a day with
3
3
3
hours of sunshine.
(b)
On another day the café served
150
150
150
customers. Use the line of best fit to estimate the number of hours of sunshine on that day.
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Level 2
4 marks
Start
→
Mark as done
Eleven bean plants were measured on various days in the first week after planting. The scatter graph shows the results, with a line of best fit drawn.
1
2
3
4
5
6
7
5
10
15
20
25
days since planting
height (cm)
(a)
Use the line of best fit to estimate the height of a bean plant
4
4
4
days after planting.
(b)
Ravi wants to use the same line of best fit to estimate the height of a bean plant
30
30
30
days after planting. Explain why his estimate is unlikely to be reliable.
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Level 3
3 marks
Start
→
Mark as done
For each of 15 small shops, the number of hours
h
h
h
the shop was open on a Saturday and the shop's takings £
T
T
T
that day were recorded on a scatter graph.
The shops in the sample were open for between
4
4
4
and
9
9
9
hours, and the line of best fit has equation
T
=
45
h
+
60.
T = 45h + 60.
T
=
45
h
+
60.
(a)
Use the line of best fit to estimate the takings of a shop that was open for
7
7
7
hours.
(b)
Explain why the line of best fit should
not
be used to estimate the takings of a shop that was open for
24
24
24
hours.
(c)
Write down what the number
45
45
45
in the equation tells you about these shops.
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Level 3
4 marks
Start
→
Mark as done
A market stall trader recorded, on 13 market days, the number of hours the stall was open and the number of items sold. The scatter graph shows the results, with a line of best fit drawn.
1
2
3
4
5
6
7
8
10
20
30
40
50
hours open
items sold
(a)
Use the line of best fit to estimate the number of items sold on a day when the stall was open for
6
6
6
hours.
(b)
Find the gradient of the line of best fit.
(c)
Interpret the gradient of the line of best fit in the context of this question.
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Level 3
4 marks
Start
→
Mark as done
The scatter graph shows the number of hours of exercise per week and the resting pulse rate, in beats per minute, of 14 students. A line of best fit has been drawn.
1
2
3
4
5
6
7
8
55
60
65
70
75
80
85
90
95
hours of exercise per week
resting pulse (bpm)
(a)
Use the line of best fit to estimate the resting pulse rate of a student who exercises for
5
5
5
hours per week.
(b)
Sam says the estimate in part
(a)
must be reliable, because
5
5
5
hours is inside the range of the data. Comment on Sam's statement.
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Level 4
4 marks
Start
→
Mark as done
The scatter graph shows the number of hours of sleep and the reaction time, in milliseconds, of 13 people. A line of best fit has been drawn.
4
5
6
7
8
9
10
200
210
220
230
240
250
260
270
280
hours of sleep
reaction time (ms)
(a)
Use the line of best fit to estimate the reaction time of a person who slept for
9
9
9
hours.
(b)
A person has a reaction time of
250
250
250
milliseconds. Use the line of best fit to estimate the number of hours that person slept.
(c)
Explain why your answer to part
(b)
is only an estimate.
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Level 4
4 marks
Start
→
Mark as done
A candle is lit and its length is measured once an hour for the first
6
6
6
hours. The results are plotted on a scatter graph and a line of best fit is drawn. The line has equation
L
=
20
−
2
t
,
L = 20 - 2t,
L
=
20
−
2
t
,
where
L
L
L
cm is the length of the candle and
t
t
t
is the time in hours since it was lit.
(a)
Use the line of best fit to estimate the length of the candle after
4.5
4.5
4.5
hours.
(b)
Work out the length that this line of best fit predicts after
15
15
15
hours.
(c)
Use your answer to part
(b)
to explain why the line of best fit should not be used to make a prediction for
15
15
15
hours.
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Level 4
5 marks
Start
→
Mark as done
A company owns 13 machines. The scatter graph shows the age of each machine, in years, and the amount spent on repairing it last year. A line of best fit has been drawn.
1
2
3
4
5
6
7
8
100
200
300
400
500
age (years)
repair cost (£)
(a)
Find the gradient of the line of best fit.
(b)
Use the line of best fit to estimate the amount spent last year on repairing a machine that is
5
5
5
years old.
(c)
Interpret the gradient of the line of best fit in the context of this question.
(d)
The company also owns a machine that is
20
20
20
years old. Explain why the line of best fit should not be used to estimate the amount spent on repairing that machine.
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Level 5
6 marks
Start
→