Student: Ritu Tiwari

Q. What is the significance of Mean, Median and Mode. What they are used for practically?

Answer :

Ritu,  Thanks for your question.  

Yes many students get confused the differences between mean, median and mode and their significance. Here is the concept and explanation which would help in understanding it better.

Topic: Statistics

Concept : With a large data set, it  would be  helpful  if entire data set can be represented with a single value that describes the average value of the entire set. In statistics, that single value is called the central tendency and mean, median and mode are all ways to describe it.

In simplistic terms, 
Mean is an  Average. The mean is a way to describe the "middle" so that numbers far from the middle have a bigger influence than numbers close to it. 

Median is the middle term after sorting.

Mode is the most frequent presence. 

Method :
Mean : To find the mean, add up the values in the data set and then divide by the number of values that you added. That`s the mean. Mean is also commonly known as average.
Median : This one is very easy.  Take the set of numbers, put them in order from smallest to largest, or vice-versa, and then pick the one that is exactly in the middle.  
That`s the median. 
Median has the property that half of the data points are below it and half are above it. 
Mode : This is really simple.  Say If you have a set of numbers, then the mode is the number appearing most frequently.  It really doesn`t matter if the most frequent number is the smallest in the list, the largest, or anywhere in the middle.  If it shows up on the list the largest number of times, it is the mode.

Example : 
Let`s take following data set and find mean, median and mode.
Date Set :  8, 4, 3, 7, 2, 9, 8, 1, 5, 13, 6  
Total data points are 11 
Mean : Add all data points and divide by total data points.
Mean : (8 + 4 + 3 + 7 +  2 + 9 + 8 + 1 + 5 + 13 + 6)/ 11 
On solving,  Mean = 66/11 
Hence Mean = 6 

Median : Arrange in ascending order and pick the middle term.

On arranging the data set looks like : 
1, 2, 3, 4, 5, 6, 7, 8, 8, 9, 13 
Middle term is 6. 
So Median is 6. (Note : Mean, Median, Mode can be same)

Mode : Find the most frequent term in the data set. 
Date Set :  8, 4, 3, 7, 2, 9, 8, 1, 5, 13, 6 
On looking at data set, the number 8 occurs most time. 
Hence Mode is 8  
Isn`t it simple Ritu !!!

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