- Descriptive statistics, inferential statistics.
- Distinguish Between a sample and a population

** two main branches of statistics**

- descriptive statistics
- inferential statistics.

**statistical analysis**

- any statistical analysis, the key is to understand your data and frame questions based on data.

**What is statistics?**

- statistics is being redefined as the art of learning from data.
- learning from data, it includes that you want to seek some information from data.
- So, Sheldon Ross defined statistics as the art of learning from data, you are concerned with collection of data, subsequent description and their analysis which often leads to drawing of conclusion.
- So, the main idea of statistics and statistical analysis is to actually draw conclusions based on data.

**classification of statistics**

- one way you are describing data that is a part of statistics which is concerned to description and summarization of data more popularly referred to as the descriptive statistics branch.
- The part of statistics which is concerned with drawing conclusions from data is called the inferential statistics branch that is you want to infer from data
- Now, when you want to infer from data, there is one very important thing which is the possibility of chance

because when you are inferring from data there is an element of chance you do not have

**inferential statistics**

- So, primarily when you talk about inferential statistics, we are trying to talk about drawing of conclusions from data.
- Now, a branch of inference as inferential statistics,

one important thing is many a time you are interested perhaps in knowing about the percentage of all students in India who have passed their Class 12 exams and study

engineering; - the prices of all households in Tamil Nadu;
- the total sales of all cars in India in the year 2019; the age distribution of people who visit a city Mall in a particular month.
- So, one way of answering all these questions is one is through a complete enumeration – you go and collect data on everybody or everything you are interested.
- For example, in this question you are interested in knowing about the percentage of all students in India,

but very quickly you understand that getting this kind of data might not be very easy. - So, many a time what we are interested in knowing is the percentage of all students in India.
- Now, if I just want to construct a database and I would want the actual data of all the students who have passed class 12, but if my intention is just to know an overall feel of what are the kind of people who finally, end up taking engineering then one thing I would want to know is work with a smaller subset of all the students in India.
- All the set of all students in India is what we refer to as a population.
- A smaller subset of this is referred to as a sample.
- It is a subset, so, I am putting it as a sample.

**Representative**

- Now, many a time you might be wanting to know about the prices of all houses.
- Again, you need not go and find out about all the houses that have been sold in a particular year;
- you might want to know about a smaller subset of the entire population.
- One thing you want about the sample is you want it to be as representative as possible you want the sample to be as representative as possible.

**what do we mean by representative sample?**

- population is a collection of all elements that we are interested in.
- suppose this is a population and I take another subset here.
- Suppose I take a subset, this is a subset.
- The smaller set is actually a subset of the larger set, but we very quickly notice that the smaller set does not have any yellow elements in it.
- So, I cannot say this smaller set is actually a good representative sample of the larger set.
- So, a sample is basically a subgroup of the population that will be studied in detail.

**what is the purpose of statistical analysis?**

if the purpose of your analysis is just to examine and explore information for its own intrinsic interest only, this study is descriptive.

Now, what do we mean by that? Let me demonstrate it to you through a data set ok.

- This is again another hypothetical data set which is just showing the names of the cricket players.
- The matches they have played, in what role, what are the total runs, the batting average,
- the highest score, wickets, bowling average and best bowling.
- Now, suppose a purpose is just to understand what are the total runs scored, what is the batting average, what is the who has the highest batting average, who has the highest run scored, who have played the most number of matches, if these who has taken the highest

number of wickets - if these are the questions of interest then all these questions of interest which I have just posed now, can directly be just got from the data set.
- I might also want to order the number of runs of a batsman has scored;
- I might want to also know what is among the batsman how have the people scored runs and all of this I

can just describe this data. - I do not have to do anything more about this data. So, in this case the question I am asking is basically, the purpose I have here the purpose I have here is to just examine and explore the information that is given.
- So, the study is just descriptive.
- I am not asking anything more. I just want to describe the data set that is given here and this study is descriptive.

**Sample**

- suppose I am using this and one thing which we notice again in this data is the following.
- If you look at this data this data is not the entire cricketing data about all the cricketers available from all the countries.
- It is a sample from an entire population of data. It is just a small sample.
- I can say it is at best a representative sample of the Indian cricketing data over the last 5 or 10 years or

perhaps about this could be about for the in the last decade. - It is a sample of definitely, it is a sample of the Indian cricketing data.
- But, it is again not the entire population which includes over all batsmen and overall cricketers, but however, if I am just interested in summarizing this data if my inherent interest is just about summarizing this data, then I would be interested in only a descriptive nature of studies for which descriptive statistics is sufficient.

**Inferential Statistics**

- Now if I am going to use this to draw a conclusions further conclusions;
- for example, if I want to know about the role a batsman plays with a batting average, I would need more information and I want to pick up a team for the future.
- For example, you we all know about the IPL auctions and how people are chosen.
- So, there is a further
- role. I am just not interested in describing this data.
- The bigger role for me or the bigger interest for me is to use this data to gather or infer some information which I am going to use in my decision making process.
- For that I would I am going to have an element of chance and there I am going to have what I need

is I am going to have an inferential study in that case.

**Inferential Statistics and Descriptive study**

- descriptive study we need to understand whether our nature of a study is only going to be descriptive or whether we want to do an inferential study.
- descriptive study it might be either performed on a sample or on a population.
- We need to understand whether a descriptive study is performed on a sample or on an entire population that is the reason why we introduced the notion of a sample and a population at this stage.
- However, if our inference is to be made about a population based on the sample, then the

study becomes inferential.

**summary**

- the two main branches are descriptive statistics,

inferential statistics. - You are going to do a descriptive study or inferential study based on what is your purpose of study.
- If your intrinsic purpose is just to summarize your data, you would go for an descriptive statistic.
- But if your purpose of study is to infer into the future or infer about a larger population using a smaller subset, you would go for inferential statistic.
- To do understand inferential statistic, you need to understand what is the concept of a population and sample.

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