# Mathematics Principles V11

Clive W. Humphris

DATA ANALYSIS: Frequency Distribution. Data Analysis is the name given to the investigation of numerical relationships within large quantities of statistical data. Within this program we can make use of the computer random number generator to avoid having to input many data values. In this first example we generate a bar chart of 100 values, showing their frequency of occurrence.

From this data we can determine the statistical measurements of 'mean', 'median' and 'mode'. Follow the calculations by clicking the calculations toolbar button, this will show how each is found using the given formula.

The 'mean' is simply the average of all the values. However, when the sample data range is limited to just a few values, i.e. 0 to 9, it's most likely that two or more of these values have the same number of occurrences. In this case either or all these values are then valid for 'mode'.

The 'median' is the value of the middle number of a set of numbers. When there is an even number of values the median is the average of the two middle values. Two methods of calculation are shown. For greater accuracy use the second formula. The simple calculation is only valid if the distribution of the sample values is symmetrical about the mean, but the more complex formula applies when there is a moderate skew in the distribution curve.   