Methods for summarising data
1.
For each set of data given below, find the range, interquartile range, and the
semi-interquartile range.
a)
32
30
36
27
24
33
34
29
b)
10
12
11
9
9
13
10
11
7
11
9
8
c)
9
10
3
7
8
5
4
7
4
3
6
2
2
a) Find the range of the following set of board game scores:
8
18
7
16
19
8
11
18
10
14
11
15
16
24
b) For the same data find:
i)
the upper and lower quartiles
ii)
the interquartile range
iii)
the semi inter-quartile range
22
9
3
For each of the populations shown below calculate or estimate, as appropriate,
the mean and the standard deviation:
a)
12
10
8
20
6
13
7
9
25
15
b)
Number (x)
1
2
3
4
5
6
Frequency (f)
3
7
10
14
8
2
c)
Class
10-14
15-19
20-24
25-29
30-34
Frequency
2
8
14
10
6
4.
A class of 6 children sat a test; the resulting marks, scored out of 10 were as
follows:
4
5
6
8
4
9
Calculate the mean and the variance of this population.
5.
Ten machines had to be fitted with new microchips. The time taken (in
minutes) for each fitment was as follows:
51
49
56
60
52
58
49
56
52
57
Calculate the mean time taken and the variance of this population.
6.
Each student in a small Higher Education College sat the same examination.
The marks were recorded and the following grouped frequency distribution
produced:
Mark
Frequency
1 – 20
8
21 – 30
30
31 – 40
90
41 – 50
103
51 - 60
79
61 – 70
64
71 – 80
21
81 - 90
5
Estimate the mean and the standard deviation of these marks for this
population.
7.
A health clinic wished to check the daily milk consumption of its 160 clients.
Each client recorded their intake of milk (in ml) during a given day. The
results were summarised as follows:
Milk intake
Number of clients
0 – 24
2
25 – 49
6
50 – 99
42
100 – 149
56
150 – 199
22
200 – 299
22
300 – 499
10
Estimate the mean and the standard deviation of the milk intake of this
population.
8.
The number of errors, x, on each of 200 pages of typescript was monitored.
The results when summarised showed that:
x = 920
x2 = 5032
Calculate the mean and standard deviation of the number of errors per page.
9.
A sample of students sitting a entrance examination for the civil service has
the following distribution of verbal reasoning (V.R.) scores
V.R. scores
80-99
100-109 110-119 120-129 130-139
Frequency
17
50
250
120
55
Using a suitable code work out the mean for this data.
140-149
8