A measure of central tendency is done to represent a dataset using its summary statistics. There are three different central tendency measures which can be stated as Mean Mode and Median. So, there may be a query about why we need other central tendency measures when only Mean can be used to complete the job. Let us check in this article about why different central tendency measures are taken and the definition of each measure with examples.
Example of a Dataset
Let us take an example with a dataset consisting of coins. Let us assume that there are 5 people in the room with the names A, B, C, D and E. A has a total of 20 coins in his wallet, B has 15 coins, C has 18 coins, D has 12 coins and E has 15 coins. Now we need to find the central tendency using Mean, Median and Mode.
After finding the calculations, we would later try to check the central tendency behavior by adding a data point to the data set used. This would help us realize the importance of central tendency measures and its application in different conditions.
Calculation of Mean using the Dataset
From the above dataset we can say that there are 5 people with respective amounts of coins in their wallets. If we plot the numbers against a line, it would display only the distance from the reference point which is 0 in our case.
So, if we put them in ascending order, the number of coins could be represented as variables.
X1 = 12, X2 = 15, X3 = 15, X4 = 18, X5 = 20.
Now by using the formula, Σ Xi/N, where i represents the number from 1 to N and N represents the total number of data points. Mathematically, it also represents the average of all the points from the origin.
Therefore, the mean of the dataset can be calculated as:
(12 + 15 + 15 + 18 + 20)/5 = 16. Thus, the mean of the dataset is 16 coins.
Calculation of Median using the dataset
Steps to Follow:
- We need to put the data points in ascending order.
- Now, we have to cross-sectionally split the data points so that one half remains on the right while the other half remains on the left. Assume this as a separator separating data points into two halves.
- If there are odd numbers of data points, then there would be one value for the separator. If there are even numbers of data points, then we need to find the average of the two data points lying on either side of the separator. This would be the median.
In the above dataset, there are 5 data points A, B, C, D and E. By putting them in ascending order we get, D=12, B=15, E=15, C=18, A=20.
Thus, there are 5 odd data points in the above dataset. Thus the median would be represented using the middle data point within the set. Here, E or B would be the median which is 15.
Calculation of mode using the Dataset
Mode is the easiest central tendency to calculate. The trick is to find the frequency of occurrence of the data points. Mode can be represented as the highest frequency within the dataset.
In the above example, there are 5 different data points consisting of different number of coins. If we look into the dataset carefully, we would find that B and E both have 15 coins with them. Thus, here the highest frequency in the dataset is 15. This is termed as the mode of the dataset.
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