Analyzing data: Exploring Moments, Skewness, Kurtosis ---

Description

Bringing you more learning in Statistics through this course. The target audience could be students of Applied Mathematics or Statistics, or anyone interested in Statistics. A good knowledge of Statistics is of immense use in Economics and Actuarial Sciences and this course helps prepare you.

The course starts with the definition of Moments and Skewness. You will learn about Moments of a distribution-There are 4 moments that are explained here. These are the Central Moments .Problems of the type-

Calculate the first 4 central moments for 2,3,5,7,8 are discussed. You will also learn how to calculate the same for a frequency distribution.

We then move on to Skewness. Skewness and Kurtosis is taught here .Skewness is defined as the lack of symmetry of a curve. Two types of skewness are discussed. Karl Pearson's coefficient of skewness is discussed.

You will learn how to calculate Karl Pearson's coefficient of skewness for a frequency distribution. If the mean, mode and standard deviation of a frequency distribution are 27.5, 30, 7.2 respectively, calculate Karl Pearson's coefficient of skewness. Problems of this type are solved here.

The next lesson teaches you more about Skewness. Bowley's coefficient of skewness is discussed. For a frequency distribution if the 3 quartiles are given, you will learn how to calculate Bowley's coefficient of skewness.  You will be taught how to calculate Bowley's coefficient of skewness for a frequency distribution. Kurtosis is introduced here.  We start with Kurtosis definition. Kurtosis is defined as a measure of the shape of the frequency curve. Mesokurtic, Leptokurtic and Platykurtic curves are discussed here. For a mesokurtic distribution , the standard deviation is 0.4. Calculate the 4th central moment. Problems of this type are discussed. If the first 4 central moments of a distribution are 0,2.4, 0.6 and 17.25. Examine the Skewness and Kurtosis of the distribution. This is another illustrated problem here.

The last lesson is on Correlation and Rank Correlation. You will learn how to calculate the Correlation Coefficient. Correlation is defined as the relationship between two variables x and y. We start with the definition of Covariance. You will learn how to calculate covariance between 2 variables given their sum , product of sums and total number of variables. You are then introduced to Karl Pearson's coefficient of Correlation which helps to standardize the covariance formula. If the covariance of 2 variables is given , and the variance of the 2 variables is given, how will you find the correlation coefficient? Watch this lesson! You will be taught how to calculate Karl Pearson's coefficient of correlation for 2 variables x and y. If we give ranks to the two variables either in ascending or descending order, you get Spearman's Rank Correlation coefficient. How to calculate Spearman's Rank correlation coefficient for 2 variables is taught here. What happens if a rank is repeated? Watch this lesson to find out!

Get a basic introduction to Inferential Statistics. Learn basic terms such as sample mean, sample proportion and sample standard deviation. Also, learn what is interval estimation.

You'll learn about confidence intervals and confidence values. How to calculate the interval estimation for the population mean and population proportion are taught here. It is useful to remember some standard confidence values which are explained here.

Explore the magical world of hypothesis testing, where you'll learn about null hypothesis and various parameters for accepting or rejecting it.

This is followed by t distributions , how to calculate the t values using the table and using the t values to accept or reject a hypothesis.

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