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Measures of Central Tendency

Statistics introduce Measures of Central Tendency. It is used in almost all the processes that we do daily. An Analyst must have a sound knowledge of Statistics as it helps them make effective decisions related to business plans. Data Science usually depends on the Measures of Central Tendency. If you tend to become a fine Data Scientist, you must be thorough with all the Measures of Central Tendency. Central Tendency is defined as the descriptive summary of the collected data set where a single value represents the whole data. Measures of Central Tendency come into the picture when you require representing your data collection into a single value. 

For Example,

Here is a scorecard,

The Central Tendency of the above example is:

92+74+80+864= 83

Hence, the Central Tendency is 83.

Central Tendency is also known as the Measures of Center. It plays a vital role in plotting the data among the frequency distribution. It indicates the general shape of the distribution and provides a better idea of how the numbers are grouped. You can use several Statistics methods to represent the center of the distribution. Through Central Tendency Statistics, you will see the distribution of the data with the involvement of the dispersion or variability. Thus, the width of the bell curve is the source that gives you an idea of the amount of dispersion in your data. This process allows you to determine whether the data has a strong or weak Central Tendency. Hence, dispersion and the general shape of your curve play an essential role in deciding the Central Tendency of your data.

Central Tendency can be calculated over three types of series.

• Individual Series : It is a series of data consisting of single values.

• Discrete Series : It is a series of data that includes values and the frequency of the values given.

• Continuous Series : It is a series of values that continually have frequencies.

There are three main types of Measures of Central Tendency:

• Mean: The mean is the most popularly used Measure of Central Tendency. It is the ratio of the sum of the terms to the numbers of the terms. In terms of Data Science, for ungrouped data that have not been grouped in the intervals, the arithmetic mean here is the sum of all the values in the population data divided by the number of all the values present in the population data. For grouped data, the mean is calculated by an approximation using the midpoints and the frequencies of the distribution. 

• Median : Median divides the distribution into halves, and it is also known as the value at the 50th percentile in the distribution. The median location can be found by the formula (N+1)/2, where N is the number of data present. Suppose N is 7, and according to the formula, the median will be 4. Suppose N is 6, then according to the formula, the median is 4.5, which means the median lies between 4 and 5. Median distributes the data in such a manner where an equal amount of data lies on either side of the median and sometimes indicates the value of the data set, which can be extremely high or low. You will find this result while working on the non-normal data.

• Mode : Mode is the frequently used Measure of Central Tendency. It is also the common score in the distribution that corresponds to the highest point on the distribution. If you find multiple highest frequencies, then the distribution is said to be multimodal. For example, in the distribution 22,44,66,44,88, the most frequently appeared number is 44, which becomes the mode of your data. In terms of Data Science, the mode will help you recognize the frequently occurring value from the entire population data set. It is not always necessary that the mode value should always appear at the center of the data set. Suppose there is no frequently occurring value. It indicates that there is no mode for that particular data set. The mode can also be multimodal, like a bimodal or a trimodal. Mode is often utilized as the only central value by the experts for analysis purposes. 

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