Measures of Central Tendency

Measures of Central Tendency

Measures of central tendency provide a way to summarise data using a single value.

Mean

• The mean is the most common measure of central tendency. It is calculated by adding up all the data points and dividing by the total number of data points.
• It is sensitive to outliers (values far from the rest), which can significantly alter the mean.
• It is best used for data without extreme values.

Median

• The median is the middle value when all data points are arranged in order of magnitude.
• If there’s an odd number of data points, the median is the middle value. With an even number of data points, the median is the average of the two middle values.
• The median is not affected by outliers and provides a central position of the data, but it doesn’t take into account the exact values of each point.
• This is useful for data with extreme values or skewed distributions.

Mode

• The mode is the most frequently occurring value in a data set.
• It is possible to have one mode (unimodal), more than one mode (multimodal), or no mode at all (no repeated values).
• The mode is easy to find in a data set, but it may not provide a good measure of central tendency for continuous or large data sets.

Choosing the appropriate measure

• Mean is best for symmetric distributions without outliers (such as a normal distribution or a bell curve).
• Use the median for skewed distributions and for data with outliers.
• The mode is useful with nominal data or for finding the most common item.
• Ultimately, the choice of measure depends on the nature of the data and the specific analytical goals.