Definition of Central Tendency
Central Tendency Definition states that the central tendency in mathematics is the average value of the data that is widely distributed. It refers to the central or middle value of the data distribution. Thus central tendency is also called as centrality. We can also define central tendency as the tendency of the quantitative data to cluster or group around a central value. Hope this definition gives an idea of what is central tendency.
Measures of Central Tendency
The ways by which the central tendency in math can be measured or calculated is termed as measures of Central Tendency. The various measures of central tendency are arithmetic mean, median, mode, geometric mean, harmonic mean, weighted mean, distance-weighted estimator, truncated mean, midrange, midhinge, trimean, and winsorized mean.
Central tendency statistics is taken using any one of the above measures for any analysis that has to be carried out by taking statistics of a sample or whole data. The appropriate method is chosen based on the context of the data population for which central tendency in mathematics has to be measured. For example, for data with underlying order, median is used to measure the central tendency. If the given data is based on measurements, then arithmetic mean is used to calculate central tendency in math. In some cases, the data that is to be analyzed does not fall under both the categories i.e. data is neither a measurement or has underlying order. In such cases where data is nominal, the central tendency measure “mode” is used.
Result of applying wrong measure of Central Tendency
Let us look at few examples of central tendency and discuss about what happens if the appropriate measure of central tendency is not chosen. Let us take a case of one of the measure of central tendency, the arithmetic mean. This measure, as the name implies, is applied in cases where the statistics has to be calculated by finding out the average of the given arithmetic data. But there are some cases where the difference between the data values is more in which case application of this measure i.e. the mean fails to give the correct statistics.
Let us consider an example of a teacher teaching 2 students. The teacher needs to know the effectiveness of her teaching. For that, the average of the marks of the two students in a test is taken. Suppose the marks of the two students are 10 and 90, then mean can be calculated by adding the two numbers and dividing it by 2. The average obtained will be 50, which means both are average students. But the reality is: one student is below average and the other one studies well.
Thus choose the right measure that is appropriate to the statistics to be taken.
