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Descriptive Statistics

In general terms descriptive statistics do just what the name implies… they describe things!  There are two variables descriptive statistics entails:

1) central tendency and

2) spread or dispersion.

The Mean

The most common measure of central tendency is the mean or average.  To calculate the mean, the data points are added and then divided by the number of data points.

An important point is that the mean should only be used when the data is from a normal distribution.  If, for example, the data is from an exponential distribution (e.g. most “time” related metrics) the mean should not be taken to describe its central tendency.  Instead, the median should be used.

The Median

Let’s say we have the following data set: 1, 9, 11, 22, 9, 1, 6, 1, 2 and desire to know the median. Here is how we do it.

1. Sort the data in descending order: 22, 11, 9, 9, 6, 2, 1, 1, 1
2. Find the middle of the data set which will be the median: The integer 6 is in the middle and is our median.

If there are an even number of data points, the two numbers that comprise the center are averaged since there will not be one single number dead in the middle.

The median is generally used when dealing with skewed distributions.  The most common example is home prices.

Since there are always a few “expensive” homes in the neighbourhood the distribution is often skewed.  This makes using the median more appropriate since these “outliers” are not able to skew the result.

The Mode

The least used measure of central tendency is the mode.  The mode is simply the most frequent value in a data set.  Using the example above {22, 11, 9, 9, 6, 2, 1, 1, 1} the mode would be 1 since it occurs more times (3) than any other number.

MS Excel Tips

Excel can be used to figure these out for us.  Here is how:

1. For the mean use the following: =average(data set)
2. For the median use the following: =median(data set)
3. For the mode use the following: =mode(data set)