Student Question

What do you mean by the term Central Tendency? What are the characteristics or properties of a good measures of Central Tendency?

Expert Answers

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There are three basic ways to measure central tendency: mean (average), median (the data point that is in the middle of a list of data listed from least to greatest), and mode (the data point that occurs most often).

The mean is best used when the data contains no outliers (items that are very different than the rest of the data).  To calculate the mean, find the sum of all the data points.  Then divide by the number of data points.

The median is best used when the data does contain outliers.  Arrange the data items from least to greatest and then find the item that is in the exact middle of your list.  If there is an even number of data items, you will have two items in the middle of your list.  Find the mean of these two items to obtain the median.

The mode is only useful when the data is non-numerical.  For instance, in a survey asking for a group's favorite color, the mode would be the best measure of central tendency.

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Central tendency can be evaluated using either the arithmetic mean, or median and mode. The evaluation of central tendency with one of the three measures depends on the constraints with regards to the set of data whose central location needs to be established.

The most used measure of central tendency is the arithmetic mean. The arithmetic mean of values in data set is given by the summation of all the values in data set, divided by the cardinality of the data set.

`bar x = (Sigma_(k=1)^n x_k)/n`

Since the evaluation of central tendency depends on the constraints with regards to the set of data, you need to identify when the other two measuring methods are more appropriate to be used. For example, when data is skewed, the mean is unable to predict the central tendency, hence, it is indicated to use the median to evaluate the central location, since median is not affected by the skewed data.

While the mean is the most commonly used in evaluation of central tendency, the mode is the least method when finding the central location. The mode can be used to evaluate the central tendency only when data set contains nominal variables.

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