STATISTICS WORKSHEET
1. The marks obtained by 30 students in a Mathematics test are shown below.
5
8
3
5
7
6
2
9
8
5
2
5
4
8
9
1
5
6
3
7
9
2
5
6
5
3
8
1
5
4
(a) Complete the following frequency table for the data given.
Mark (x)
1
Tally
Frequency (f)
xxf
2
2
2
3
4
5
6
7
8
9
[5 marks]
(b) State
(i)
The modal mark
(ii)
The median mark
(c) Using the table, calculate the mean mark on the test.
[1 mark]
[1 mark]
[3 marks]
(d) Determine the probability that a student selected at random obtained a score greater
than 6.
[2 marks]
[Total: 12 marks]
2. The table below shows the distribution of the masses of some packages.
Mass (kg)
Number of packages
Cumulative Frequency
1 – 10
12
12
11 - 20
28
40
21 - 30
30
31 - 40
22
41 - 50
8
(a) Complete the table to show the cumulative frequency for the distribution.
[2 marks]
(b) On the grid provided on page 3, draw the cumulative frequency curve for the data.
Use a scale of 2cm to represent 10 kg on the x-axis and 2cm to represent 10
packages on the y-axis.
[5 marks]
(c) Using your graph, determine the following;
(i)
The median
(ii)
The interquartile range
(iii)
The semi-interquartile range
[1 mark]
[3 marks]
[1 mark]
(d) Calculate the probability that a package selected at random has a mass:
(i)
less than 35kg
(ii)
greater than 22kg
[4 marks]
[Total: 16 marks]
3. The heights of 9 pupils, to the nearest centimetre, are given below.
156
153
159
156
158
155
152
157
151
Determine:
(i)
The modal height
[1 mark]
(ii)
The median height
[1 mark]
(iii)
The mean height
[2 marks]
(iv)
The lower quartile
[1 mark]
(v)
The upper quartile
[1 mark]
(vi)
The interquartile range
[1 mark]
[Total: 7 marks]
4. A class of 24 students threw a cricket ball at sports and the distance thrown by each
student was measured to the nearest metre. The results are shown below.
22
48
55
36
50
34
29
63
35
45
46
54
52
23
56
32
47
43
43
49
30
40
59
60
(a) Complete the first two columns of the frequency table for the data shown above.
Distance (m)
Frequency
20 - 29
3
30 - 39
5
[2 marks]
(b) For the class interval (30 – 39) m, state:
(i)
The lower class limit
(ii)
The upper class boundary
(c) Determine the class width used in the frequency table.
[ 1 mark]
[1 mark]
[1 mark]
(d) Estimate the mean distance thrown by the students. (Show your calculations using
the third column of the table).
[3 marks]
(e) Using a scale of 2cm to represent 10 metres on the x-axis and 2cm to represent 1
student on the y-axis, draw a histogram on the grid provided on page 6 to illustrate
the data.
[5 marks]
(f) Determine the probability that a student chosen at random threw the ball a distance of
50m or more.
[2 marks]
[Total: 15 marks]