In collecting data, people always want to know how to best describe the data. The first technique often used is to calculate a mean, median, and mode, three statistics that do provide description of the central tendency of the data. These statistics then provide a basis for the comparison of one group’s data to the data of another group.

The mean, median, and mode, ideally, will be the same value for an individual data set, but, in real life, this is not the case. They are often different, and can indicate if the data set is skewed one way or another when compared to the normal distribution.

The mean is often called the average, and is calculated by taking the sum of all of the values and dividing the sum by the total number of values in the set. This is one of the most useful statistics, and is commonly used in parametric statistical analysis, where the underlying distribution of the data is known. A warning for the mean: when the data set has outliers and is skewed, the mean is also skewed, and doesn’t provide a reasonable estimate of the measure of central tendency for a particular data set.

The median is the value in the middle. The median is found by first placing the values from smallest to largest. Then, for a set with an even number of values, there are two values that are considered the middle. The media is the average of these two values. For the sets with an odd number of data points, the median is the data set that is the one in the middle of the set. The median is the base statistic that is used in many non-parametric data analyses versus the mean. For a skewed data set, the median can provide a value that is the best estimate of the measure of central tendency of a particular data set, as having outlying data values will skew the mean. When the data is not skewed, the median and mean should be the same value.

The mode is the value which appears the most in a data set. It is not always the median or the mean. Sometimes, a set may have more than one mode. Ideally, however, the mode will be the same value or very close to the median and the mean of a data set.

Overall, the mean, median, and mode are useful for determining the basic descriptive of a data set. They are not always the same value, but they can be the same value. If they are the same, then they all point to the same thing: the value of the variable that is the one around which most values are likely to occur.