Exercises 1D Solutions
Question 1D.1
Carry out a 5-number summary for the data provided in Question 1C.1. Use the
information to construct a boxplot.
The data set was ordered in the solution to Question 1B.3
1
46
10
47
21
50
22
51
[23]
[60]
24
71
41
76
41
78
42
100
[45]
Since there are 19 data values, 9 lie below the mean and 9 above the mean. To find the
two quartiles we need the middle value of these two sets, namely 23 and 60. The 5number summary is therefore given by:
Low =1
LQ=23
Median=45
UQ=60
High=100
This information looks quite symmetric as a boxplot:
Question 1D.2
Find the mean and standard deviation for the following sets of data:
a)
0, 1, 3, 5, 7, 7, 9, 11, 13, 14
The mean is 70/10=7. For the standard deviation we set up the table
Value
0
Deviation from Mean
7
Squared Deviation
49
1
3
5
7
7
9
11
13
14
6
4
2
0
0
2
4
6
7
36
16
4
0
0
4
16
36
49
The sum of the squared deviations is 210. Divide this by 9 to get a variance of 210/9
and take a square root to get a standard deviation of 4.83.
b)
0, 0, 0, 0, 7, 7, 14, 14, 14, 14
The mean is 70/10=7. For the standard deviation we set up the table
Value
0
0
0
0
7
7
14
14
14
14
Deviation from Mean
7
7
7
7
0
0
7
7
7
7
Squared Deviation
49
49
49
49
0
0
49
49
49
49
The sum of the squared deviations is 392. Divide this by 9 to get a variance of 392/9
and take a square root to get a standard deviation of 6.60
Question 1D.3
A data set is such that its mean is 20, and all of its values lie between 0 and 10 or
between 30 and 40. Which is correct? The standard deviation is
a) less than 0
b) between 0 and 5
c) between 5 and 10
d) greater than 10
Since the mean is 20 and all data points lie between 10 and 20 units from this, the
standard deviation must also lie in this range. So d is correct.