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 Rev. 0