A measure of central tendency, in simple terms, is when data is obtained and analyzed to explore what is the middle of it.
When we do a central tendency analysis of data what we are doing is trying to find out what are its average, median, and, mode.
Central tendency also refers to the usual value, in other words, what something "typically" measures. For example, in a class of failing high school students, the central tendency in standardized Math tests could be a performance of 50% or less.
The mean of the data is the central tendency. In the example provided before, we can just look at the data and say that the average performance is 50% or less. However, we want to provide a clear average with specific amounts to determine a mean. For this, we add up all the scores and divide them by the numbers of test takers to get the class average. That average is the mean and the central tendency.
The median is used mostly to avoid skewing the data and as another measure of central tendency. For example, all standardized Math test of our sample group of students would be organized from least to greater. Those which are the same score will be put together under the same number. You are to find the numbers that rest right in the middle (median) of the list to determine the central tendency You can see with this information "how far of a stretch" there is between the average, the low, and the top.
Finally, the mode is the most repetitive characteristic or trend that is repeated by many people. For example, in our sample class, if the most repeated grade was a 37%, that is what gets reported as the mode.
Why do all these matter? Because it is a much better analytical way to look at the numbers that we get from the first report, and because it helps us differentiate and understand the rationale behind the numbers, and so we can find and identify the central tendencies.