IB Style Questions – Statistics
Bivariate Data and Linear Regression
Question
Score
Out of
1
6
2
6
3
6
4
6
5
6
6
6
7
6
8
19
9
15
10
14
Total
90
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1
Question 1
Consider the graph of variables
versus
shown on the set of axes below:
a.
Draw a line of best fit on the graph shown above.
b.
Circle the correlation coefficient shown below that best illustrates the relationship
shown between the two sets of data x and y.
c.
Use the line of best fit drawn in part (a) above to estimate a value of
corresponding to an value of 10.
Working……
(a) Provide solution on graph shown above.
(b) Circle the appropriate
value shown above.
(c) ____________________
(6 marks)
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Question 2
Five students were given quizzes in two different subjects,
The results are shown in the table below:
a.
and .
Student
A
B
C
D
E
Score
2
3
5
6
8
Score
3
4
5
8
8
Plot the points representing the ordered pair of scores for each student on the set of
axes shown below:
y 10
8
6
4
2
0
b. Calculate
c.
and
2
4
6
8
10
x
for the given data.
Plot the point
best fit for the data.
on the set of axes shown above and drawn a line of
Working……
(a) Provide solution on axes shown above.
(b)
(c) Provide solutions on the graph shown above.
(6 marks)
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Question 3
Match the letter of the appropriate correlation coefficient with the graphs shown below:
Graph 1:
A.
Graph 2:
B.
C.
Graph 3:
D.
E.
Working……
(a) Graph 1: ______________
(b) Graph 2: ______________
(c) Graph 3: ______________
(6 marks)
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Question 4
Ten middle years students were measured for height (
are shown in the table below:
Height:
and
(cm)
and arm span
Arm Span:
152
154
156
154
160
158
164
166
166
163
166
167
170
172
175
174
177
178
180
178
a.
Calculate
b.
Determine the correlation coefficient between
c.
Use words to describe the relationship between
. The results
(cm)
.
and
and
.
.
Working……
(a)
____________
____________
(b) ____________________
(c) ______________________________________________________________
______________________________________________________________
(6 marks)
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Question 5
A data collection for 20 IB students compares their percent scores on the IB HL English A
exam ( ) and the verbal score ( ) of a college entrance exam (the SAT).
The correlation coefficient between variables
and
is
. The following is also known:
and
And the regression equation for the line of best fit between
where
and
is given by
is a real number constant.
a.
Determine the value of
.
b.
Use your result from part (a) above to predict the college verbal entrance exam
score for a student who scores 75% on the IB HL English A exam.
Working……
(a) ____________________
(b) ____________________
(6 marks)
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Question 6
The table below shows a data collection for seven students. It compares amount
of time
on average per week that each student spends working out in the
school gym per week versus the percent body fat
per student.
Student
Time per week ( ) –
hours in gym
Body Fat ( ) percent
A
B
C
D
E
F
G
1.5
2
3
4.5
5
6
7.5
15.5
14
12
12.5
11.5
10
9.5
a.
Calculate the correlation coefficient between
correct to 2 significant figures.
b.
The regression equation for the two variables is given at follows:
where
Find
c.
and
and
. Write your answer
.
.
Use your result from part (b) above to predict the percent body fat
of a student who works out at the gym 4 hours per week.
Working……
(a) ____________________
(b) ____________________
(c) ____________________
(6 marks)
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Question 7
A data collection consisting of 30 primary years students shows their body
weight
in kilograms versus the distance
in meters they can run in 60 seconds.
The correlation coefficient between variables
known:
and
is
. The following is also
and
And the regression equation for the line of best fit between
where
and
is given by
is a real number constant.
a.
Find
.
b.
Use your result from part (a) above to predict the distance
with a weight
of 45 kg.
run by a student
Working……
(a) ____________________
(b) ____________________
(6 marks)
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Question 8
The table below shows the results of a fitness test given to six middle years students.
Each student has corresponding scores for cardiovascular recovery time
in seconds
after a six minute run along with the distance in centimetres recorded for a standing jump.
Student
Recovery Time
sec
Jump Distance
cm
a.
b.
-
A
B
C
D
E
F
300
420
500
270
600
480
190
175
160
200
140
170
Draw and clearly label a scatter diagram for the data shown. Use
a scale of 1 cm per 50 seconds on the horizontal axis for recovery
time
, and start your scale at 250 seconds. Use a scale of
1 cm per 10 cm on the vertical axis for distance
jumped, and
start your scale at 130 cm.
[5 marks]
Determine the equation for the line of best fit of the data points. Express
your equation in the form:
D  aT  b , where
[4 marks]
c.
Calculate the correlation coefficient of
d.
Draw the calculated line-of-best-fit on the scatter diagram from
part (a) above.
[3 marks]
Determine the nature of the relationship shown (direct or inverse)
and write a general statement describing the relationship.
[2 marks]
Use your equation for the line-of-best-fit to predict the distance
jumped by a student who has a recovery time of 450 seconds.
Write your answer accurate to one decimal place.
[3 marks]
e.
f.
versus .
[2 marks]
[19 total marks]
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Question 9
A group of six grain products was tested for fat and for fiber content at a food production
laboratory. A 100 g sample of each food was tested. The following results were found.
Food
Fat
A
B
C
D
E
F
a.
b.
c.
12.5
6
4
9.5
8
11
Fiber
1.5
4.5
8.5
5
5.5
2
Construct and clearly label a scatter diagram for the given data.
Use the horizontal axis to represent fat content ( ) and use the
vertical axis to represent the fiber content ( ) . Clearly label an
appropriate scale on each axis.
[5 marks]
Calculate the mean values and for each group. Plot the point
on the scatter diagram and clearly label it with the letter M .
[3 marks]
Determine the the equation of line-of-best-fit for the given data.
Write your answer in the form
where ,
Write the values of
and
accurate to three significant figures.
[3 marks]
d.
Draw the line of best fit on the scatter diagram from part (a) above.
[2 marks]
e.
Use the line-of-best-fit drawn to determine an approximate value of
fiber content from a grain food type having a fat content of
.
[2 marks]
[15 total marks]
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Question 10
a.
A recent study was made to compare the vitamin C intake of students
in elementary school (grades 1 to 6) versus the student's ability on a
general mathematics test. The scatter diagram of results is shown below:
Vitamin C Intake vs Mathematics Ability Test Score
60
Math Test
40
Score
20
0
150
200
250
300
350
400
450
Vitamin C per day (mg)
An IB student in Mathematical Studies reviewed the data and made the
following comment:
The scatter diagram of the data comparison clearly indicates an inverse
relationship between the two data variables. Furthermore the high positive
correlation found shows that vitamin C intake is clearly a determining factor
for the ability level achieved in mathematics at this school. In simple words,
"Taking vitamin C causes an increase in math ability."
Critically comment on the conclusion made by this student. Make direct
reference to any facts that have been misinterpreted.
[4 marks]
problem continued on next page . . .
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b.
Data was recorded for quizzes taken in two different subjects and
for a group of students. Results of the data analysis are shown below:
(i)
Calculate
and
[4 marks]
(ii) The regression equation for the variables
as:
where
and
can be written
.
Determine the value of .
(iii) Describe in words the relationship between the variables
[3 marks]
and .
(iv) By using your result from part (b. ii) determine a value of the
variable that would correspond to a value of
.
[1 mark]
[2 marks]
[14 Total Marks]
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12