STATISTICS
Higher Concepts of Mathematics
Example:
A test was given and the following grades were received: the number of students
receiving each grade is given in parentheses.
99(1), 98(2), 96(4), 92(7), 90(5), 88(13), 86(11), 83(7), 80(5), 78(4), 75(3), 60(1)
The data, as presented, is arranged in descending order and is referred to as an ordered
array. But, as given, it is difficult to determine any trend or other information from the
data. However, if the data is tabled and/or plotted some additional information may be
obtained. When the data is ordered as shown, a frequency distribution can be seen that
was not apparent in the previous list of grades.
Grades
Number of
Occurrences
Frequency
Distribution
99
98
96
92
90
88
86
83
80
78
75
1
11
1111
11111 11
11111
11111 11111 111
11111 11111 1
11111 11
11111
1111
111
1
1
2
4
7
5
13
11
7
5
4
3
1
In summary, one method of obtaining additional information from a set of data is to determine
the frequency distribution of the data. The frequency distribution of any one data point is the
number of times that value occurs in a set of data. As will be shown later in this chapter, this
will help simplify the calculation of other statistically useful numbers from a given set of data.
The Mean
One of the most common uses of statistics is the determination of the mean value of a set of
measurements. The term "Mean" is the statistical word used to state the "average" value of a set
of data. The mean is mathematically determined in the same way as the "average" of a group
of numbers is determined.
MA-05
Page 2
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