I have invested my funds in 6 stocks resulting in 6 different returns. I can calculate the average of returns i.e. called mean. Every time it’s not necessary you will get your mean return, sometimes it will deviate from the mean and it can be checked by standard deviation, variation etc. So, it is very important to have an in depth knowledge in statistics to play with data. In FRM-I quant’s have 20% weightage in the exam.

Basic Statistics

Simply defined, statistics is a problem solving field of study and knowledge involving collection, organization, analysis, interpretation and presentation of data.

Importance of statistics

You might have wondered at one point of time “why do I need to learn statistics?” or “When exactly will I use it?” You will find the answers in this session on Basic Statistics which will allow you to analyze the vital role statistics play in every field of human activity. It can be employed almost everywhere ranging from business, economics, mathematics, banking, accounting and auditing etc.

Statistics will arm you with the basic tools you require in order to react intelligibly to information you hear or read. Let us be more specific and look at some of the daily life scenarios in which we make certain claims which have been possible only because of statistics.
• Women make 80 cents to every dollar a man makes when working in the same job.
• There is an 85% chance that in a room full of 40 people that at least 3 people will share the same birthday.
• A newly released research shows that eating egg whites can increase one’s life span.
• Almost 80% of lung cancers in men and 30% in women are tobacco related.
• Native Europeans are more likely to be hit while crossing the street as compared to people of other ethnicities.

All the above claims are statistical in nature and have come from diverse areas like psychology, health, law etc. Statistics is useful in lending credibility to an argument.

• In business world, in order to make quick and spontaneous decisions, statistics play a major role.
• Using statistics, one can plan production according to customer liking and wants.
• One can check products’ quality way more efficiently with statistical methods.
• It provides a quantitative basis for arriving at business decisions.

Having understood the usage of statistics in real world, let’s now move a step further and see the basic stats’ measures necessary to evaluate the data at hand.

Measures of Central Tendency

It is a single value that shows and describes a set of data by determining the central point within the set of data. It is for this reason, it is often called measures of central location. Measures of central tendency includes mean, median, and mode, but each have different functionality for different data set. To estimate the central point of a sample, it can be measured by:

Mean: This measure can be used for any discrete and continuous data, more often for continuous data. It takes into account all the values in your data set as a part of the calculation.
Let’s understand its disadvantage with a hypothetical case:

 Worker Salary 1 4000 2 4200 3 4000 4 12700 5 13400 6 4100 7 4000 8 4500 9 4700

The mean salary is 6177 whereas if we have a deep introspection we would see the majority of the population lies in the 4000 – 4500 salary range. The mean is skewed by the two large salaries. In situations like this mean doesn’t represent the accurate data.

Median: It is the middle most value or score which has been arranged in an order of magnitude. It is not affected by skewed / extreme values. Let’s understand median with the help of a real life application:
If a house broker is estimating current rates prevailing in a particular area, he / she may use median to get an approximate valuation for the same place.

 House Price House1 20 Lacs House2 27 Lacs House3 22 Lacs House4 21 Lacs House5 29 Lacs House6 26 Lacs House7 24 Lacs House8 28 Lacs House9 22 Lacs

So, to derive at any conclusion the data needs to be arranged in ascending order:

 House Price House1 20 Lacs House4 21 Lacs House3 22 Lacs House9 22 Lacs House5 29 Lacs House7 24 Lacs House7 24 Lacs House6 25 Lacs House2 27 Lacs

Total number of observations are 9 so middle observation being 5th i.e. House 7 which is priced at 27 Lacks would be considered as median.
Mode: is one the most popular measures of central tendency and it shows the most frequent value occurring in a data set. For example, it can be used in a shoe manufacturing company in real life. If studies from mode shows, size 7 and size 9 footwear are sold the most, then the manufacturing company can produce more of those sizes.
To summarize the measures of central tendency lets a quick look at its benefits and drawbacks:

Measures of Central Tendency
Mean All data used for finding answer Very large and small numbers can alter the answer
Median Extreme values doesn’t affect it Time consuming for large data set
Mode We can still use the data even if the data is non numerical • There may be more than one mode
• If none of the data are same, there may not be any mode at all

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