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## What questions can statistics answer?

Question: I am sure you are using a mobile phone! Aren’t you?

Question: Did you ever hear that it is hazardous for your health?

Research says:

• Radiation received by the human body through the earpiece is likely to affect the brain of the human being – some experts opine.
• Some say that this would happen if the earpiece is less than a certain distance from the ear
• Others say that the danger only arises if the mobile is used for more than five minutes at a stretch.

Question: How do we come to a conclusion?

Answer: In such a case, Statistics come to your rescue!

Besides the medical science involved in the above decision, huge data in the form of the persons using the mobile phones, their age, their way of living, place of using the mobiles, duration of the use, extent of battery charge available in the mobiles etc. can be collected and analyzed before doctors take over to form an opinion in the matter.

## So what are statistics?

Modern storage and analytical capabilities have greatly increased the complexity of data. To make any decision, important or unimportant, one has to analyze the available data on that subject. And the only tool available to analyze all this data is called statistics.

Numerous examples can be cited from daily life to show us to how one cannot take a prudent decision without using this tool:

• Launch of a product in the market for which one would require various market research data coming in the form of tables (product wise or feature wise)
• Investing in a stock or mutual fund, for which one has to analyze the data like its earnings or its P/E ratio etc. or
• Decision whether one should pursue an MBA

As is clear, all these decision making processes require data analysis by using Statistics. No wonder, statistics are given great importance in every portion of analytics. CFA® any other professional examination which has a stress on Analytics lays a strong foundation for statistics.

Two branches of statistics are:

1. Descriptive Statistics: to describe data.

2. Inferential Statistics: to make inferences and also use hypothesis.

## What is the use of statistics?

Let us take an example, let us assume that we need to find the optimum age for having the maximum earnings from a group of people. We have data for 1 million people in the form of records relating to their age, sex and income.

If there is a person of age 11 has an income of \$90, a person of age 21 years has an income of \$5600 dollars. There would be one billion such records and to interpret this huge data would be a stupendous task. However one has to find ways to meaningfully interpret this large amount of data.

Making any judgment based on the raw data is called the descriptive statistics and it plays a very important role.

In order to simplify the things, we can form groups. In this particular case, groups with various ages are formed. Group 1 covers the 10-20 years age group; Group 2 covers the 20-30 years age group and so on. For the first group, average income is \$100, for the second \$10,000. We can similarly take different age groups and count their frequency. As age increases first, the income increases; then it starts decreasing and then it remains constant. And may be the maximum is achieved around 45.

We can show this data in the form of a graph or a table. There are various methods to represent the collected data which are:

• Graphical displays of the data in which graphs summarize the data or facilitate comparisons
• Tabular description in which tables of numbers summarize the data
• Summary statistics (single numbers) which summarize the data

In a nutshell, various step used in Statistics can be summarized as follows:

• Collect data: in the form of a poll, a questionnaire or whatever other means
• Classify data: as per frequency distribution tables
• Summarize data: so that the average and variance groups could be found and it is clear as to how to I represent this data
• Present data: in terms of graphs
• Proceed to inferential statistics if there is enough data to draw a conclusion.

## What is ‘real life’ application of Statistics?

The following application has been taken from the University of Melbourne paper to conclude that all parents have shorter children, on average.

Sir Francis Galton (1822-1911) was the first to note that tall parents have shorter children, on average. His protege and colleague Karl Pearson (1857-1936) studied 1078 father-and-son pairs. He found that the fathers’ average height was 68 inches and the sons’ average 69 inches. However, the tall fathers (say, of height 72 inches, within the vertical strip on the graph below) had sons averaging 71 inches. They were one inch shorter, on average. On the other hand, the sons of short fathers (say, 64 inches in height) averaged 67 inches in height. They were three inches taller, on average. Galton termed this phenomenon “regression to mediocrity”. Ever since, the method of studying how one variable relates to another variable has been called regression analysis.

The figure shows the heights of 1078 fathers and their sons at maturity. Each father is paired with only one of his sons. Fathers and sons of equal height lie along the solid line on the figure (x=y).

The figure is based on a graph from Statistics by Freedman, Pisani, Purves and Adhikari.

CFA Program is the gold standard in education and lays a strong foundation on Quantitative Analysis and understanding the principles of Statisics. If you are interested in gaining a fundamental stronghold on your finances, you can consider enrolling for the CFA examination. More details about the examination can be obtained by sending an email to info@edupristine.com or calling +91 989 298 0608