Measures of Central Tendency

Measure of Central Tendency is a summary statistic that represents the center point or typical value of a data set. It describes the characteristics of your data set.

There are three Measures of Central Tendency: Mean, Median and Mode.

Mean is the average of the data set. To get the average of the set, we start by getting the sum of all the data over n as the number of data in the set.

Mean is the most important statistic in data because it is the center of gravity of your data set which means it carries a piece of information from every member of the sample. It also serves as basis in conducting and understanding other complex statistics.

To simply understand this, here is an example: 9, 7, 6, 13, 5, 9, 2

This is the data set, each data in the set is being separated with a comma (,). To get the average, you just have to add all these data, so we have this: 9 + 7 + 6 + 13 + 5 + 9 + 2 = 51. After adding all the data, we have to divide the sum by the number of data in the set. So, let’s count how many data are in the set. We have 7, so we will divide 51 by 7 and we will get a result of 7.29. So, the average or the mean of this data set is 7.29

Median is a simple Measure of Central Tendency because it simply is the middle data in the set. In finding the median, it is a must to arrange the data in order either from least to greatest or vice versa because the purpose of median is to separate the lower from the upper half of the data set.

For example, we have a data set of 5, 9, 13, 2, 9, 6, 4. Let's arrange it in order, we now have this data set: 2, 4, 5, 6, 9, 9, 13.

Now, the process in getting the median will depend on the number of data in the set. If the number of data is odd, then the middle data is simply the median.

With the example that we have here, the number of data is 7 which is odd and the middle data is 6. So, the median in this data set is 6.

Now, what if we have an even number of data. Let’s say we have this set: 5, 9, 7, 13, 6, 9, 2, 3. If the number of data is even, we have to get the average of the 2 middle data to get the median. So, let's areange this in order, we get: 2, 3, 5, 6, 7, 9, 9, 13 and the 2 middle data that we have here in this set are 6 and 7. We have to get the average of 6 and 7, so 6 + 7 is 13 then we divide 13 with the number of data that we added which is 2. 13 divided by 2 is 6.5. The median in this data set is 6.5.

Mode is the data that appears the most often in the data set. It shows the most frequent or common data in the set. It describes the characteristic of the data set.

For example,

We have this set: 5, 2, 9, 3, 5, 1, 4.

It can be confusing if we will not arrange the data in order. We might miss some numbers especially if we have a lot of data in the set.

So, what I usually do is arrange the data in order which will give us this: 1, 2, 3, 4, 5, 5, 9. As you can see, it is much easier to identify the mode if it is in order.

So here, 5 appeared twice compared to others that only appeared once. 5 appeared most often, therefore, 5 is the mode in this data set.

What if we have: 3, 9, 1, 7, 3, 9

Arrange the data in order, you should have this: 1, 3, 3, 7, 9, 9. And here, we can see that 3 and 9 are the modes in this data set because both appeared twice or most often compared to others.

So, yes, we can have two modes or more. If it has one mode, we call it unimodal. If it has two modes, we call it bimodal. If it has three modes, we call it trimodal. If it has more than three modes, we call it multimodal. These are the different types of mode we can use to describe a data set. Based on the previous example where we had two modes in the data set. We can say that the data set is Bimodal.

Now, I have another example. What if we have this set: 2, 1, 5, 3, 2, 4, 5, 9, 5

If you can observe, it is quite confusing especially if there are more than 2 data that are appearing often. So, let’s arrange this in order, we get this: 1, 2, 2, 3, 4, 5, 5, 5, 9.

Here, it shows that 5 appeared three times, therefore, 5 is the mode of this data set.

How about these 2 examples?

A. 1, 3, 4, 5, 8, 9

B. 3, 7, 0, 2, 1, 0, 5, 4

Set A has no mode because there is no data that appeared most often while Set B has a mode which is 0 because 0 appeared most often in the data set. Don’t confuse yourselves with these 2 data sets because in statistics or with other branches of mathematics, zero has its own value.

We can relate this topic on this Coronavirus situation that we have right now. Can you recall the first few weeks where coronavirus just spread in our country? DOH had a number of coronavirus patients and it formed a cluster around the age gap of 60 to 69 years old. This age gap 60 to 69 years old is the mode in their coronavirus positive cases chart. People in this age group are prone to this coronavirus illness.

WHO identified the median to determine the incubation period for this illness and they found out that the time between exposures to the virus and showing symptoms is around 5 days. These are just basic examples where we can apply measures of central tendency.