Measures of Central Tendency

The measure of central tendency is a value that represents the average of a list of numbers or a central point of a dataset. It tells the point where the data points in a dataset are most concentrated. They help a lot in statistics and data analytics. Measures of central tendency are very important in the field of business analytics.

In this tutorial, I will answer all your measures of central tendency questions. This should give you a better picture of the main types of measures of central tendencies.

Types of Measures of Central Tendency

There are mainly 3 types of measures of central tendency mean, median, and mode. In this section of the tutorial, let me discuss the different measures of central tendencies along with their measures of central tendencies formula.

Mean

Mean is the most commonly used measure of central tendency. Mean is the arithmetic average and is calculated by making a sum of all the values in the given set and subsequently dividing it with the number of values. The sign "𝑥" (pronounced as "x-bar") or "𝜇" (pronounced as "mu") is often used to represent the mean of a dataset.

Let me show you an example of measures of central tendency by demonstrating how to calculate the mean of a given dataset.

Source: twitter

In the above formula, n is the number of elements present in the list. There are two steps in the above formula. The first step is adding all the numbers in a dataset. The second step is to divide the sum by the number of elements.

Let me show you an example to help explain this better. For example, let me take a list of numbers 1, 4, 3, 5, 6, 4, 5, 3, 9.

Step 1: First, we add all the numbers to find the summation.

1 + 4 + 3 + 5 + 6 + 4 + 5 + 3 + 9 = 40

Step 2: We then count the number of elements in the given dataset. In this case, it is 9.

Step 3: we then divide the total sum by the number of elements in the list(n).

This is given by 40/9, which comes to around 4.44. Thus 4.44 is the approximate mean of the given list.

Median

Now let me tell you about the median. The median function only works with datasets that are sorted. It gives the midmost value in a set of values of numbers ordered in an ascending or descending order. Unlike the mean, which represents an arithmetic average, the median will not be affected by extreme values and is most applicable when data is biased or contains outliers.

Let me teach you how to calculate the median of a set of numbers. There are two ways you can use to calculate the median. The method you use depends on the number of elements the given dataset has.

Source: SatisticsHelp

For an odd number of data points

For an odd number of points,

• We first sort the data points in either ascending or descending order.
• The median is the midpoint value. For example, if you have nine data points, the median will be the fifth value after sorting.

For an even number of data points

For an even number of data points,

• The first step remains the same. We sort the data points in either ascending or descending order.
• Find the average of the two middle values. For example, if you have ten data points, the median will be the average of the fifth and sixth values after sorting.

Advantages of Median

Let me discuss some of the pros of using the median as a measure of central tendency. The advantages of using the median are as follows.

• Extreme values impact the median less than the mean, making it more robust and appropriate for datasets with outliers or skewed distribution.
• The median represents the central value that splits the dataset into two equal portions, making it an accurate representation of the data's middle value.
• The median is very useful when it comes to ordinal data or data with ranking categories, when the average or arithmetic mean may be meaningless.

Mode

Mode is the least used measure of central tendency among the three. The mode is a measure of central tendency that finds out the most common value or category in a dataset. The mode is especially useful for categorical data or datasets when determining the most common value is important.

Now let me teach you how to calculate mode with the help of a couple of examples.

In the first data set, the numbers are 5, 23, 6, 9, 5, 4, 9, 5. In this list, 5 is repeated 3 times. This makes the frequency of 5 in the list the highest thus making it the mode of the list.

• Similarly, in the second list, both 5 and 9 are present thrice in the list. This means both 5 and 9 are the modes of the list. There can be more than one mode in a dataset.

Uses of Measures of Central Tendency

The application of measures of central tendency is very diverse. Here in this section of the article, let me discuss some of them with you one by one.

• Measuring central tendency helps in comparing various sets of data. For instance, the mean of the income of different groups of people will help to find out the differences in their buying habits and many such things.
• Descriptive statistics use measures of central tendency. They provide a summary of where points are concentrated in a dataset. This helps us understand the distribution and features of the dataset better.
• Measures of central tendency provide a reference point around which data points are concentrated. This helps analysts to make sense of a data set and draw inferences.
• Measures of central tendency are also used in prediction and forecasting. It can be used as an input to statistical models. These models predict outcomes like future trends and results. For example, by finding out the historical mean, we can predict accurately future sales of a company and so on.
• Quality assurance uses measures of central tendency quite heavily. It is used to assess the quality of the products and the stability of the process. For example, calculating the mean defect rate of a process may help us where the process is lacking and aid in making it better.
• Decision-making is strongly affected by measures of central tendency. Measures of central tendencies help us make smart choices after carefully considering the data we are given. For example, we can compare projected mean sales and actual mean sales and try to find out corrective measures we can take to better the company.
• Measures of central tendency are a boon for risk analysis and management. We evaluate certain situations by finding out the average central tendencies. This information helps us make decisions to reduce risk.

In Conclusion

Summing it up, measures of central tendency are a very useful tool. It helps us in a lot of ways like making informed decisions, avoiding risk, quality control, and much more. However, it is important to keep in mind that not all the measures of central tendency are the same. The three types of central tendency mean, median, and mode have different use cases. We need to be careful and use the right tools in the right situation.

This tutorial on measures of central tendency has given you an idea of where to use which measure of central tendency. If you want to learn more about statistics and data analytics, I would recommend doing a certified course on this subject. One platform that I cannot recommend enough is upGrad. Their courses are in collaboration with some of the best universities around the world. Some of the best professors curate the courses.

Frequently Asked Questions

1. What are the measures of central tendency in data analysis?
Measures of central tendency are mathematical functions used to describe a dataset's center or average. There are mainly three measures of central tendency.

• Mean
• Median
• Mode

2. What is central tendency in descriptive analytics?
In descriptive analytics, central tendency refers to the average or central value around which the majority of data points are present. It gives a summary of where the data points are centered or concentrated. Mean, median, and mode are the most popular measures of central tendency used in descriptive analytics.

3. Which of the following measures the central tendency of data?

There are only three types of commonly used measures of central tendency. They are mean, median, and mode.

4. What are the measures of central tendency for qualitative data?

The measure of central tendency used for qualitative data is mode. Qualitative data is data that contains categories or groups. Unlike numerical data, which can be operated upon by means and medians, the idea of an average or middle value is not directly applied.

5. What are the 4 measures of central tendency?

The four measures of central tendency are.

• Mean
• Median
• Mode
• Midrange

5. What central tendency means?

In statistics, the central tendency is a statistical measure identifying the location of a dataset's center or usual value. It summarizes the core, or average, value around which the data points cluster.

7. Which is best measure of central tendency?

There is no one best measure of central tendency. It depends on a lot of factors: data structure, distribution of values, presence of outliers, and specific goals of the analysis. Each measure of central tendency(mean, median, and mode) has its own set of pros and cons for application, depending on the context and goals of the analysis. 

8. What is the formula of measure of central tendency?

There are 4 formulas for the 4 different types of central tendency. The different formulas apply for mean, median, mode, and midrange. 3 of them are discussed above in the tutorial.