Statistics - Measure Of Central Tendency

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Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of DATA. Statistics is applied to a Scientific, Industrial or Social problems.  Statistic has been extensively used in the field Of Genetics or Bio Statistics to be precise. Statistics helps us to gain insights from the Data of any kind.

 Image by GraphicMama-team from Pixabay 

DESCRIPTIVE STATISTICS

In this blog we will hover over DESCRIPTIVE STATISTICS, which describes or summarizes characteristics of the data, it consists of two basic categories Measure of Central Tendency and Measures of Variability. This section will deal with Measure of Central Tendency.

POPULATION VS SAMPLE

Population in general means the number of people in a country or a specific place however, In Statistics, Population means a collection of people, collection of objects, collection of numbers, collection of observations , collection of instances or a collection of anything (data) that needs to be analysed.

For Example: - If a research is done on mice, then the population refers to every single mouse in the collection.

 Image by GraphicMama-team from Pixabay 

SAMPLE

Experiments or Research is usually done on the Sample Data, Sample data is taking some random observations or instances or data from the Population. Taking out few observations from the population and conducting research on the Sample population and concluding the results/inferences for the whole population.

For Example: - Taking some mouse from the population of mice for the purpose of research or experiment and finding the results for the whole population.            

                                                                                Image by GraphicMama-team from Pixabay 


                                                                                                                                

Why do we Take Samples out Of Population?

Performing researches on complete population is not feasible and very exorbitant process. As we are living in the world where lot of Data is generated every Second, it is not possible to perform the research on the exorbitant amount of data also, sometimes gathering all the data is a difficult process and requires lot of time and resources. Hence to avoid the hassle, an extensive research is performed on the sample and the results are applied on the complete population or data.

Measures of Central Tendency

MEAN, MEDIAN, MODE are the measures of Central Tendency. We will Deal with them one by one

MEAN

We have all studied about the Mean in our School, For a Set of numbers; mean/average/arithmetic mean is a central value of a finite set of numbers. It is calculated by adding all the observations in the data divided by the number of observations.

The arithmetic mean of a set of numbers x1, x2, ..., xn is given by as :-

 


                                                                               

Population Mean

Population mean is denoted by ยต.  Population mean is calculated by adding all the observations of Population dividing by the number of all those observations.

                                                                       


Sample Mean

SAMPLE Mean is denoted by   X bar.  Population mean is calculated by adding all the observations of Sample dividing by the number of all those observations.

                                                                 

Median

Median is the middle value which divided the entire population/sample into two halves. The median is the "middle" number, when the set of numbers are listed in order from smallest to greatest. The main feature of Median is that it does not get affected by the Outliers unlike mean.

 Calculate Median

Imp Note- Set of observations has to be ordered from lowest to highest.

CASE 1:- No of observations are odd

Median of the series   10, 20, 30, 40, 50 is 30  

CASE 2:- No of observations are even

Median of the series 10, 20, 30, 40, 50, 60   is the mean of the middle two terms i.e, 30+40 = 70/2 = 35

MODE

Mode is defined as the most frequent values in data set.

 Calculate Mode

 In a data set, 1, 2,2,3,4,4,4,5,6.

 Mode will be 4.

These three are the measures of central tendency and they all tell the central point /value of a dataset. It may be also referred as the centre of the data. And hence they give insights about the central values of the data you are dealing with. They are usually used simultaneously, which is also a good idea while analysing any data. Measures of central tendency describe the center of a data set.


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