The mode is rarely chosen as the preferred measure of central tendency. The mode is not usually used because the largest frequency of scores might not be at the center. The only situation in which the mode may be preferred over the other two measures of central tendency is when describing discrete categorical data.
The mode is preferred in this situation because the greatest frequency of responses is important for describing categorical data. Joe Boyle Updated June 5, For this reason, the mode will be the best measure of central tendency as it is the only one appropriate to use when dealing with nominal data.
The median is usually preferred to other measures of central tendency when your data set is skewed i. However, the mode can also be appropriate in these situations, but is not as commonly used as the median. The median is usually preferred in these situations because the value of the mean can be distorted by the outliers. However, it will depend on how influential the outliers are. If they do not significantly distort the mean, using the mean as the measure of central tendency will usually be preferred.
If the data set is perfectly normal, the mean, median and mean are equal to each other i. The median and mean can only have one value for a given data set. The mode can have more than one value see Mode section on previous page. FAQs - Measures of Central Tendency Please find below some common questions that are asked regarding measures of central tendency, along with their answers.
What is the best measure of central tendency? It can be used with both discrete and continuous data, although its use is most often with continuous data see our Types of Variable guide for data types.
The mean is equal to the sum of all the values in the data set divided by the number of values in the data set. You may have noticed that the above formula refers to the sample mean. So, why have we called it a sample mean? This is because, in statistics, samples and populations have very different meanings and these differences are very important, even if, in the case of the mean, they are calculated in the same way.
The mean is essentially a model of your data set. It is the value that is most common. You will notice, however, that the mean is not often one of the actual values that you have observed in your data set.
However, one of its important properties is that it minimises error in the prediction of any one value in your data set. That is, it is the value that produces the lowest amount of error from all other values in the data set. An important property of the mean is that it includes every value in your data set as part of the calculation.
In addition, the mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero. The mean has one main disadvantage: it is particularly susceptible to the influence of outliers.
These are values that are unusual compared to the rest of the data set by being especially small or large in numerical value. For example, consider the wages of staff at a factory below:. Staff 1 2 3 4 5 6 7 8 9 10 Salary 15k 18k 16k 14k 15k 15k 12k 17k 90k 95k. The mean is being skewed by the two large salaries.
Therefore, in this situation, we would like to have a better measure of central tendency. As we will find out later, taking the median would be a better measure of central tendency in this situation. Another time when we usually prefer the median over the mean or mode is when our data is skewed i.
If we consider the normal distribution - as this is the most frequently assessed in statistics - when the data is perfectly normal, the mean, median and mode are identical. Moreover, they all represent the most typical value in the data set. However, as the data becomes skewed the mean loses its ability to provide the best central location for the data because the skewed data is dragging it away from the typical value.
However, the median best retains this position and is not as strongly influenced by the skewed values.
This is explained in more detail in the skewed distribution section later in this guide. The median is the middle score for a set of data that has been arranged in order of magnitude. The median is less affected by outliers and skewed data. In order to calculate the median, suppose we have the data below:.
Our median mark is the middle mark - in this case, 56 highlighted in bold.
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