Measures of Central Tendency: Mean, Median, and Mode

Study Notes

Measures of Central Tendency

Measures of central tendency are crucial for understanding the distribution of data and for making decisions based on statistical information. The three main measures of central tendency are the mean, median, and mode. Each measure has its own advantages and disadvantages, and the choice of which measure to use depends on the properties of the data.

Mean

The mean, also known as the arithmetic mean, is the sum of all the values in the dataset divided by the number of observations. It is the most commonly used measure of central tendency because it uses all the values in the dataset. However, it is sensitive to extreme values, particularly when the sample size is small. It is not appropriate for distributions that are skewed or for nominal or non-nominal ordinal data. Mean can be calculated for numerical ordinal data but may not provide a meaningful value, such as in the case of stage of cancer. The mean is best used for data that is symmetrical and normally distributed, as it provides an accurate representation of the central value.

Median

The median is the middle value of the dataset when the values are arranged in ascending or descending order. If there are an even number of observations, the median is the average of the two middle values. It is less sensitive to extreme values than the mean and is not influenced by skewed distributions. The median is the preferred measure of central tendency when there are a few extreme scores in the dataset, when there are missing or undetermined values, when the distribution is open-ended, or when the data is measured on an ordinal scale.

Mode

The mode is the value that occurs most frequently in the dataset. If the dataset contains multiple modes, the most common mode is chosen. If the dataset has no mode, then the mode is not applicable. The mode is the preferred measure of central tendency when the data is measured on a nominal scale, as it represents the most commonly occurring value in the dataset.

In summary, the choice of which measure of central tendency to use depends on the properties of the data, such as the level of measurement, the distribution of the data, and the presence of extreme values. It is often best to use a combination of measures to get a more complete understanding of the central tendency of the data.

Description

Learn about the three main measures of central tendency - mean, median, and mode - and understand when to use each measure based on the properties of the data. Explore the advantages and disadvantages of each measure to make informed statistical decisions.