Measures of Central Tendency

We learn what is central Tendency measures or measures of central tendency like mean or average, median, mode with the example.

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Central Tendency Measures

Central tendency is a comprehensive overview of a given set of data. That describes the central value for all population. So we can get pictures of the population instead of studying at entire data points. There are three common measure is use for central tendency. Such as mean or average, median, and mode.

They are also use individually in different situations. We are going to learn all three measures of the central tendency here and also learn how to calculate or use it.

Mean

Mean is the sum of all data points is divide by the number of data points in the given data set.If we have n number of data in the dataset which are x1,x2,…xn. then mean for it is

Formula of Mean

mean denoted by sample mean as “x bar” and population mean as Σ.

For example:
(5 + 20 + 6 + 1 + 19 + 9) / 6 = 10

As the mean use all value of dataset for calculate mean value. Thats why mean highly influence of outliers. So when you have large number of outlier (skewed data) in dataset then it’s not worthy to use as measerment.

Median

Median is the center or middle of given data points. So rearrange the data points in order and find the middle value of it. If have 9 data points then we divide 4 data point each side and get median value.

For example:
– 1 56 5 8 0 12 7 3 4

Step 1: Arrange in order
– 0 1 3 4 5 7 8 12 56
Step 2: find the middle value
– so, the median is 5.

For the odd number of data points we take the center of it but what if we have even data points? For that do the average of two center values of data points.

For example, we add 2 in our previous example
– 1 56 5 8 0 12 7 3 4 2
Step 1: Arrange in order
– 0 1 3 4 5 7 8 12 56
Step 2: find the average of the middle values
– here median is (5+7)/2 = 6

Thus the median is lightly affected by outliers and skewed data.

Mode

The mode is the most common data point in a given dataset.

For example,
– 2 5 56 4 2 92 4 2 4 1 4

Here, mode is 4. As its repeat four times.

It can have one, many or no mode in the dataset. So it’s sometimes misleading to use as a measure when we have many modes.


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