Use the mean to describe an entire set of observations with a single value representing the center of the data. Many statistical analyses use the mean as a standard reference point. The mean is the sum of all observations divided by the number of observations.
Use the median to describe an entire set of observations with a single value representing the center of the data. Half of the observations are above the median, half are below it. It is determined by ranking the data and finding observation number [N + 1] / 2. If there are an even number of observations, the median is extrapolated as the value midway between that of observation numbers N / 2 and [N / 2] + 1.
The mode is the value that occurs most frequently in a set of observations. Minitab also displays how many data points equal the mode. Mode may be used with mean and median to give an overall characterization of your data distribution. While the mean and median require a calculation, the mode is found simply by counting the number of times each value occurs in a data set.
The center of the data is the area where most values in a data set cluster. Central tendency can be described by a number of different statistics, like the mean, trimmed mean, median, or mode. Knowing the central tendency of your data is an important first step in understanding it.
Graphs like histograms, boxplots, and dotplots are useful in visualizing data's central tendency and can assist in deciding which central tendency statistic is most appropriate with a given data set.
Likewise, as distributions stray from normal and become more skewed, the standard deviation becomes more different from the distance between the mean and a typical data value.
The interquartile range is a better measure of spread for highly skewed data than the standard deviation is because the interquartile range is not affected by extreme ranges.
If your data are symmetric, the measures of central tendency (mean and median) will be roughly the same. If the data are asymmetric, the measures may be pulled toward the more extreme observations. Of the measures, the mean is more influenced by extreme values and the median is less influenced.