What is the difference between a mean, median, and mode?

The mean is the average of a data set, the median is the middle value, and the mode is the most frequently occurring value.

The mean, median, and mode are all measures of central tendency in statistics, but they each highlight different aspects of the data set. The mean, often referred to as the average, is calculated by adding up all the numbers in the data set and then dividing by the number of values in that set. It provides a measure of the overall trend in the data, but can be skewed by extremely high or low values.

The median, on the other hand, is the middle value in a data set when the numbers are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle numbers. The median is often used as a better measure of central tendency when there are outliers in the data, as it is not affected by extreme values.

The mode is the value that appears most frequently in a data set. A data set may have one mode, more than one mode, or no mode at all. The mode can be useful in certain situations, particularly with categorical or nominal data where the mean and median cannot be calculated. However, it may not provide a good measure of central tendency if the most common value is far away from the rest of the data.

In summary, the mean, median, and mode are all ways to summarise a data set using a single number, but they each have their own strengths and weaknesses. The mean is useful for data sets without extreme values, the median is better for data sets with outliers, and the mode is useful for categorical data. Understanding these differences is crucial for interpreting statistical data accurately.