How to describe data with Central Tendency in Statistics

There are two ways to describe the data they are:

1. Central Tendency
2. Measure of Spread

Central Tendency:

In statistics, a central tendency is a central or typical value of probability distribution. It may also be called a center or location of distribution. Colloquially, measure of central tendency are often called averages. The most common measures of central tendency are the arithmetic mean, the median, and the mode.

Each of these measure are used depends on circumstances. Let us take a example and understand when to use each measure.

Example:

Srikanth want to join a health club in a activity that has others in the same age group as him.  He is 22 years old. Mean ages for YOGA = 15 Yrs, POWER WORKOUT = 20 Yrs and SWIMMING = 17 Yrs. If you are Srikanth, then which among the following you would join ?

Solution: Most of the people already had an answer in your mind is Power Workout right ?. In statistics never come to conclusion without look into the data. Now let us look into the data.

Yoga class:

Here, there are 6 people are there in yoga class, and at the age of 13 one person, at the age of 15, three persons and at the age of 17, there are two persons are there.

Arithmetic Mean: Simple mean or average is collection of number divided by count of numbers in the collection

Then, the mean of the ages,

Even from data and mean of the data you can notice that none of the persons are not near to Srikanth’s age (22Yrs) so he will not join Yoga class.

Power Workout:

If you look into the data, there are no person near to the age Srikanth’s age (22 Yrs). But the shifted right side the distribution and become 20. This is because there is person at the age 90. Because of this our mean got shifted in the direction of extreme point such value is called outlier.

Outliers are the extreme values or unusual behavior or pattern that influence the central tendencies (particular mean of the data)

So, the solution for this problem is to use median. 

Median is middle value. As outlier are the extreme value therefore median insensitive to outliers.