Higher Concepts of Mathematics
STATISTICS
Solution:
The mean is
[40(4)+38(3)+36+34(2)+30+28(3)]/14= 492/14 = 35.1
The mean variance is:
1
14
40
35.1
38
35.1
28
35.1
... 36
35.1
1
14
(57.8)
4.12
From the tank mean of 35.1%, it can be seen that a 40% increase in level will statistically fit into
the tank; 35.1 + 40 <100%. But, the mean doesn’t tell us if the level varies significantly over
time. Knowing the mean variance is 4.12% provides the additional information. Knowing the
mean variance also allows us to infer that the level at any given time (most likely) will not be
greater than 35.1 + 4.12 = 39.1%; and 39.1 + 40 is still less than 100%. Therefore, it is a good
assumption that, in the near future, a 40% level increase will be accepted by the tank without any
spillage.
Normal Distribution
The concept of a normal distribution curve is used frequently in statistics. In essence, a normal
distribution curve results when a large number of random variables are observed in nature, and
their values are plotted. While this "distribution" of values may take a variety of shapes, it is
interesting to note that a very large number of occurrences observed in nature possess a
frequency distribution which is approximately bell-shaped, or in the form of a normal
distribution, as indicated in Figure 1.
Figure 1 Graph of a Normal Probability Distribution
Rev. 0
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MA-05
