10APPA Semester Two Exam Revision
6. Statistics
Question 1 (CA)
Two sets of data are given below:
Set A:
15
72
35
72
41
72
43
76
43
76
48
78
52
78
52
78
57
80
59
83
63
85
65
85
65
87
67
87
72
Set B:
35
83
41
83
67
83
67
83
72
83
72
85
74
85
74
85
74
85
76
87
76
89
76
93
76
78
78
a) State the five-number summary for each data set.
Set A
Set B
b) State the range and interquartile range (IQR) for each data set.
c)
Set A
Range:
IQR:
Set B
Range:
IQR:
Identify, with mathematical reasoning, if there are any outliers in either of the data sets.
Set A
Set B
d) Construct a parallel boxplot that displays both data sets A and B on the scale provided below.
e) Which data set had the higher scores overall? Justify your answer using summary statistics.
Question 2 (CA)
For the same data sets from Question 1, complete each of the following parts.
a) Group each of the data sets into appropriately sized class intervals and hence complete each of the
following frequency tables.
Set A
Class Interval
Set B
Frequency
Class Interval
Frequency
b) Construct a histogram to display each data set on the axes provided below.
c) Use the frequency table and/or histogram to complete the following statistics for each data set.
Approximate Mean
Set A
Set B
Median Class Interval
Modal Class Interval
Question 3 (CA)
For the same data sets from Question 1, complete each of the following parts.
a) Display both data sets into a back-to-back stem-and-leaf plot.
Set A
Set B
b) Determine the mean and mode for each data set.
Set A
Set B
Mean
Mode
c) By now, you have constructed a box plot, a histogram and a stem-and-leaf plot for the same data. List
some of the benefits and limitations of displaying data in each type of graph.
Box-Plot
Histogram
Stem-and-Leaf Plot
Question 4 (CF)
Describe the relationships between the two variables in each of the following scatter-plots in terms of
strength, direction, and form.
a)
b)
c)
d)
e)
Question 5 (CF)
The scatter-plot below shows the relationships between the weights of 26 different cars and their fuel
consumption. The line of best fit has also been drawn.
a) Describe the general relationship between the two variables.
b) Use the line of best fit to predict the fuel consumption for a
car that weighs 1200 kg. Comment on the reliability of this
prediction.
c) Use the line of best fit to predict the weight for a car that
consumes 3L of fuel per 100 km travelled. Comment on the
reliability of this prediction.
Question 6 (CF)
The total number of pies sold per quarter from years 2018-2020 by a particular pie shop are shown in the
table below.
a) Construct a line graph to display this data.
Year
2018
2019
2020
Quarter
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
Number of pies
540
1200
1380
430
590
1400
1600
600
610
1620
1700
610
b) Draw a line of best fit through the data. Hence, predict the number of pies this shop can expect to sell
in the fourth quarter of 2021. Comment on the reliability of this prediction.