Analysis of Asset Allocation

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Financial Statistics: Descriptive statistics Mean

DEFINITION

Descriptive statistics are all around us. You meet them everywhere and it would be difficult to go through a full week without using them. Can you imagine watching of football game or a golf tournament where no one kept score? 

Let's take a look at the most basic form of statistics, known as descriptive statistics. This branch is the foundation of all statistical analysis. Even if some concepts are directly used in finance (e.g. to measure volatility in options,...), it is important for you to understand them if you want to efficiently manage a diversified portfolio.

The purpose of the descriptive statistics is to give you a clear view of raw data. To meet that objective, a full range of indicators has been developed and you will find here after a definition of the most important ones.

MEAN

Mean is probably the most common indicator. The mean can be defined as as the arithmetic average of all values. The mean measures the central tendency of a variable.


where
n      is the sample size.

As it is the case for all statistical indicators, the mean should not be used alone, but well with other indicators that will give you an idea of the dispersion of the data around the mean.

To illustrate that concept, let's compare two companies with 5 employees and an average salary (mean) of $10,000 

Company 1

Employee1: $ 1,000
Employee2: $ 1,500
Employee3: $ 2,000
Employee4: $ 2,000
Employee5: $ 43,500

Company 2

Employee1: $ 8,000
Employee2: $ 9,000
Employee3: $ 10,000
Employee4: $ 10,000
Employee5: $ 13,500

Even if the two companies have the same average salary, we can easily see that they are equally distributed around the mean. We will capture the distribution with the next indicators.

Do you want to know more on the subject? Visit our selection of books

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