Question

how are the measures of central tendency and variability used to analyze a data distribution

Answer 1

They help to tell easily about the data. They are more of representatives of a large size of data.

It might be very hard to tell about what we have found in the collected data. That’s the core purpose of using statistics. Central tendency and Dispersion/measures of variability are two statistics that are frequently used to describe data. These are :descriptive statistics' because they can help us to describe the data.

1. Central Tendency :

Mean, median and mode

These are most popular measures of central tendency. Their purpose is to summarize huge data with a single number. Suppose we have data on height of students in your class.

How do we make sense of the data ? We can read each height recorded and come to a conclusion about how tall students generally are in the class . But this would be time consuming also not very specific . Imagine if the class has 200 or 300 students!

In this scenario we use central tendency . It's also called measure of location. Mean for example is the average . Mode is the point with highest repeat. Median is the middle most value. So these mean , median or mode would give us one or just a few numbers. They make understanding your data easy.

2. Measures of Variability/Dispersion

Range, variance and standard deviation

It's important to know the spread of heights within the collected data. Why is it important ? Because if the spread is very high the central tendency(mean , mode , median etc) might be far from many heights. And im that case we will look at the maximum and minimum. Range, variance and standard deviation tell about the spread . Like central tendency, they also give us one or just a few numbers.