Worksheet 10.1

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Maths Quest Maths B Year 11 for Queensland
Chapter 10 Summary statistics WorkSHEET 10.1
WorkSHEET 10.1 Summary statistics
1
These data give the amount of weekly pocket
money given to a student for 8 weeks:
Name: ___________________________
2
Find the mean of the pocket money.
(b)
Find the median of the pocket money.
(c)
Find the mode of the pocket money.
This frequency table shows the sick days taken
by the workers in a factory in a month.
Mean =
(b)
$5.00, $5.20, $5.80, $5.90, $6.40, $6.50,
$6.80, $6.80
$5.90  $6.40
Median =
2
= $6.15
(c)
Mode = $6.80
(a)
(b)
(c)
Find the mean number of sick days per
worker.
Find the median number of sick days per
worker.
Find the mode for the number of sick
days.
4
5
Number of sick Frequency
days (x)
(f)
0
8
1
6
2
4
3
2
4
4
5
3
6
3
Totals
30
Number of sick Frequency
days
(f)
0
8
1
6
2
4
3
2
4
4
5
3
6
3
(a)
Sum of 8 weeks' pocket money
8
$48.40
=
8
= $6.05
(a)
$5.80, $6.40, $5.00, $6.50, $6.80, $5.90, $6.80,
$5.20.
(a)
1
fx
0
6
8
6
16
15
18
69
69
30
= 2.3 sick days per worker.
Mean =
(b)
Median = 2
(c)
Mode = 0
Maths Quest Maths B Year 11 for Queensland
3
This grouped frequency table shows the area of (a)
farm lots in hectares.
Area (ha)
30405060708090-
(a)
(b)
(c)
(d)
4
Chapter 10 Summary statistics WorkSHEET 10.1
Frequency
3
2
8
6
3
1
2
Add the midpoint x, frequency times
midpoint f  x and cumulative frequency
columns to the table. Write down the sum (c)
of f and f  x columns.
(d)
Find the mean area of the farm lot.
Find the median area of the farm.
Find the mode.
Find the range of each of the following sets of
data.
(a) 2, 5, 4, 5, 7, 4, 3
(b)
103, 108, 111, 102, 111, 107, 110
(c)
2.5, 2.8, 3.4, 2.7, 2.6, 2.4, 2.9, 2.6, 2.5,
2.8
5
Frequency
Area (ha)
(f)
303
402
508
606
703
801
902
Totals
25
(b)
2
Midpoint
(x)
35
45
55
65
75
85
95
fx
105
90
440
390
225
85
190
1525
Cumulative
frequency
3
5
13
19
22
23
25
1525
25
= 61 ha
Mean =
Median group is 50–60 ha
Modal group is 50–60 ha
(a)
Range = 7 – 2
=5
(b)
Range = 111 – 102
=9
(c)
Range = 3.4 – 2.4
=1
3
Maths Quest Maths B Year 11 for Queensland
5
Chapter 10 Summary statistics WorkSHEET 10.1
Use the frequency distribution tables below to
find the range for each of the following sets of
scores.
(a)
Score
Frequency
89
12
90
25
91
36
92
34
93
11
94
9
95
4
3
2
(a)
Range = 95 – 89
=6
(b)
Range = 180 – 150
= 30
(b)
Class
150 – 155
155 – 160
160 – 165
165 – 170
170 – 175
175 – 180
6
7
Frequency
12
25
38
47
39
20
The number of goals scored by a team is shown 4, 4, 5, 5, 7, 9, 12, 14, 16, 16
below:
(a) Lower quartile = 5
5, 4, 4, 7, 5, 9, 12, 14, 16, 16.
(b) Upper quartile = 14
(a)
Find the lower quartile.
(b)
Find the upper quartile.
(c)
Find the interquartile range
The stem-and-leaf plot below gives the exact
masses of 24 packets of biscuits. Find the
interquartile range of the data.
Key:
248 | 4 = 284.4 g
Stem | Leaf
248 | 4 7 8
249 | 2 3 6 6
250 | 0 0 1 1 6 9 9
251 | 1 5 5 5 6 7
252 | 1 5 8
253 | 0
(c)
3
Interquartile range = 14  5
=9
Lower quartile = 249.6
Upper quartile = 251.55
Interquartile range = 251.55 – 249.6
= 1.95
3
Maths Quest Maths B Year 11 for Queensland
8
Chapter 10 Summary statistics WorkSHEET 10.1
Use your calculator to find the standard
deviation of the set of outcomes when a
six-sided die is rolled as shown below.
Standard deviation = 1.87
4
1
1, 2, 3, 4, 5, 6
State your answer correct to 2 decimal places.
9
A supermarket chain is analysing its sales over
a week. The chain has 15 stores and the sales
for each store for the past week were ( in
$million):
1.5 2.1
1.4 1.6
10
2.4
2.0
1.8 1.1
0.7 1.2
0.8
1.7
0.9
1.3
3
1.1
(a)
x = 1.44
(b)
Population, as the sales from every store
are considered.
(a)
Calculate the mean sales for the week.
(b)
Should the population or sample standard
(c)
deviation be used in this case?
(c)
What is the value of the appropriate
standard deviation?
 = 0.48
The following frequency distribution gives the x = 1825
prices paid by a car wrecking yard for a sample s = 797.03
of 40 car wrecks.
Price ($)
0 – 500
500 – 1000
1000 – 1500
1500 – 2000
2000 – 2500
2500 – 3000
3000 – 3500
Frequency
2
4
8
10
7
6
3
Find the mean and standard deviation of the
price paid for these wrecks.
2

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