Assessment Solutions
Pg 149 #15
a) A data management teacher has two classes whose midterm marks have identical
means. However, the standard deviations for each class are significantly
different. Describe what these measures tell you about the two classes.
The class with the higher standard deviation has marks with a greater spread than the
other class. This means that there may be more high or low marks in this class. It
may also mean that a few extremely high or low marks are increasing the standard
deviation. In the class with the lower standard deviation, the marks will have less
spread, meaning that there is more clustering of the data around the mean.
b) If two sets of data have the same mean, can one of them have a larger standard
deviation and a smaller interquartile range than the other? Give an example or
explain why one is not possible.
Yes it is possible.
Consider the following example
Set A :
Set B:
35
52
Mean
Standard Deviation
Interquartile range
55
53
58
54
59
55
Set A: 60
12.1
7
60
60
61
65
62
66
65
67
85
68
Set B: 60
6.2
13
If you notice Set A has a larger standard deviation but a smaller interquartile range.
This is obtained by keeping the majority of the data values close to the mean, but
having a large extreme low and high points to make the spread large
Set B on the other hand has a large interquartile range but the first and fourth quartile
are more clustered reducing the standard deviation.
Pg 153 #20
Dr. Simba’s fourth-year class in animal biology has only 12 students. Their Scores
on the midterm examination are shown below
50 71
65
54
84
69
82
67
52
52
86
85
a) Calculate the mena and median of these data
50  71  65  54  84  69  82  67  52  52  86  85
x
Mean
12
 68.08333
Median = 68
b) Standard Deviation
n

(X
i 1
i
 X )2
n
(50  68) 2  (71  68) 2  (65  68) 2  (54  68) 2  (84  68) 2  (69  68) 2  (82  68)2  (67  68)2  | (52  68) 2  (52  68) 2  (86  68) 2  (85  68) 2
12
 13.87253
 14

Interquartile Range 83-53=30
Semi-Interquartile range =15
The semi-interquartile range and the standard deviation are very similar.
c) The standard deviation would be a good method to choose, as the interquartile
range is quite high,