Mean, Median, Mode and Range

• “Mean, Median, Mode and Range” are considered the basic measures of central tendency and dispersion in statistics.

• The mean is the average value of a data set. It’s calculated by adding all the values together and dividing by the number of values. An important feature is that every value in the dataset affects the mean.

• The median is the value in the middle when the data set is arranged in ascending or descending order. If there’s an even number of data points, the median is the mean of the two middle values. This measure is not affected by extreme values or outliers.

• The mode is the value that appears most frequently in a data set. A data set may have one mode (unimodal), two modes (bimodal), more than two modes (multimodal), or no modes at all (no mode).

• The range is the difference between the highest and lowest value in the data set. It is a measure of dispersion, which indicates how spread out the values are. However, it is sensitive to outliers and does not provide information about the dispersion within the dataset.

• When comparing datasets, consider using the mean and range together, or the median and interquartile range (not covered in this summary), as these two pairs take into account both the central tendency and dispersion of data.

• Be aware of the limitations of these statistical measures. For example, the mean is influenced by extreme values, while the mode might not be a useful measure for data sets with many different values.

• Be able to calculate these measures from raw, discrete and grouped data sets.

• Practice interpreting these measures in different contexts and understand the impact of changes to data sets on these measures (e.g. adding or removing values). For example, the mean would change if a new extreme value were added, but the median might not.

• Understand how to represent these measures graphically, for example, on bar graphs, histograms, or frequency polygons.

• Finally, be competent to not only compute these measures but also be able to interpret, compare, and make decisions with them to solve real-world problems.