Mean, Median and Variance

Mean and median both describe the location (i.e. central tendency) of one sample data. The mean is the arithmetic average, i.e.

	       x1+x2+... +xn
	mean = -------------
                     n

The median is the "midscore", i.e. the score which is exactly in the middle of all ordered scores. In other words, exactly 50% of the data are less than the median, exactly 50% of the data are larger than the median.

For symmetric data (e.g. human heights) median=mean. For skewed (i.e. asymmetric) data, mean and median could be quite different. For example, the mean income in the country of Tena-Tuva is TTD 100 (Tena-Tuva dollars), but the median income is TTD 10. What is happening? Here are the incomes of the 11 people who live in Tena-Tuva:

 9   9   9   9   9   10   11   11   11   11   1001

The one super-rich tena-tuvan (with income TTD 1001) pulls the mean income to an incredibly high TTD 100, even though the typical income of a tena-tuvan is more like 10!

The variance is the mean squared deviation of the observations from the mean. See the textbook for more info.

Use the minitab command describe to compute mean, median and variance.

[3]> minitab

 MTB > set 'traffic.data' c1
 MTB > describe c1
 
                 N     MEAN   MEDIAN   TRMEAN    STDEV   SEMEAN
 C1             49    5.306    5.200    5.276    1.275    0.182
 
               MIN      MAX       Q1       Q3
 C1          2.800    8.800    4.500    6.150