Measures of Central Tendency
There are 3 measures of central tendency
a) The mean
Some of the important characteristics of the mean are:
1. It is the most familiar and most widely used measure. Long explanations of its meaning are thus not usually required.
2. It is a computed measure whose value is affected by the value of every observation. A change in the value of any observation will change the mean value; however, the mean value may not be the same as any of the observation values.
3. Its value may be distorted too much by a relatively few extreme values. Because it is affected by all the values of the variable, the mean can lose its representative quality in badly skewed distributions.
4. It cannot be computed from an open-ended distribution in the absence of additional information.
5. It is the most reliable average to use when sample data are being used to make inferences about populations. The mean of a sample of observations taken from a population may be used to estimate the value of the population mean.
6. It possesses two mathematical properties that will prove to be important in subsequent chapters. The first of these properties is that the sum of the differences between data items and the mean of those items will be zero – i.e., (X - ) = 0. And the second property is that if these differences between data items and the mean are squared, then the sum of the squared deviations will be a minimum value – i.e., = minimum value.
b) The median
Some of the important characteristics of the median are:
1. It is easy to define and easy to understand. The computation and interpretation of the median, as we have seen, is not difficult.
2. It is affected by the number of observations, but not by the value of these observations. Thus, extremely high or low values will not distort the median.
3. It is frequently used in badly skewed distributions. The median will not be affected by the size of the values of extreme items, and so it is a better...