FOUNDATION MATHEMATICS MULTIPLE CHOICE QUESTIONS VCE

 











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MEASURES OF CENTRE AND SPREAD

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  The median, range and interquartile range The most versatile statistical tools for numerically describing the centr e and spread of a  distribution are:  the median (the middle value) as a measure of centre ;  the range (the maximum spread of the data values), and the interquartile range (the  spread of the middle half of data values) as measures of spread . While these statistical values ( median, range, interquartile range ) could be estimated only approximately from a histogram , they can be determined exactly when we use either a dot or a  stem plot .                                           MEDIAN Activity 1:  Finding the median value in a data set. Order each of the following data sets, locate the median, and record its value. (a)   2 9 1 8 3 5 3 8 1  For an odd number of data values, the median will be the middle data valu...
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DATA ANALYSIS: INTERPRETATION

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THE MEAN and STANDARD DEVIATION

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 In this section, we will look at alternative measures of centre (the mean) and spread (the standard deviation) that are only useful when working with symmetric distributions without outliers. While this may seem unnecessarily restrictive, these two measures have the advantage of being able to fully describe the centre and spread of a symmetric distribution with only two numbers. 1. The mean. The mean is the balance point of a distribution.  A general characteristic of symmetric distributions is that the mean and the median coincide. Example 1:    The balance point of the distribution is also the point that splits the distribution in half. That is, there are two data points to the left of the mean and two to the right.  The relationship between the mean and the median Whereas the median lies at the midpoint of a distribution , the mean is the balance point of the distribution . For approximately symmetric distributions, both the median and mean will be approxima...
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