Skip to main content

Why Central Limit Theorem is Important for evey Data Scientist?

The Central Limit Theorem is at the core of what every data scientist does daily: make statistical inferences about data.

The theorem gives us the ability to quantify the likelihood that our sample will deviate from the population without having to take any new sample to compare it with. We don’t need the characteristics about the whole population to understand the likelihood of our sample being representative of it.

The concepts of confidence interval and hypothesis testing are based on the CLT. By knowing that our sample mean will fit somewhere in a normal distribution, we know that 68 percent of the observations lie within one standard deviation from the population mean, 95 percent will lie within two standard deviations and so on. In other words we can say "It all has to do with the distribution of our population. This theorem allows you to simplify problems in statistics by allowing you to work with a distribution that is approximately normal." 


The CLT is not limited to making inferences from a sample about a population. There are four kinds of inferences we can make based on the CLT

1. We have the information of a valid sample. We can make accurate assumptions about it’s population.
2. We have the information of the population. We can make accurate assumptions about a valid sample from that population.
3. We have the information of a population and a valid sample. We can accurately infer if the sample was drawn from that population.
4. We have the information about two different valid samples. We can accurately infer if the two samples where drawn from the same population.

Condtions for Central Limit Theorem:

Independence.
>> The sampled obervsations must be independent
>> random sampling should be done.
>> if sampling without replacement, the sample should be less than 10% of the population.

Sample skew
>> The population distribution should be normal
>> But if the distribution is skewed, the sample must be large (greater than 30)

Important Points to remember :

The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger.

 Sample sizes equal to or greater than 30 are considered sufficient for the CLT to hold.

 A key aspect of CLT is that the average of the sample means and standard deviations will equal the population mean and standard deviation.

 A sufficiently large sample size can predict the characteristics of a population accurately.
Labels:

Comments

Post a Comment

Popular posts from this blog

Data is the New oil of Industry?

Let's go back to 18th century ,when development was taking its first footstep.The time when oil was considered to be the subset of industrial revolution. Oil than tends to be the most valuable asset in those time. Now let's come back in present. In 21st century, data is vigorously called the foundation of information revolution. But the question that arises is why are we really calling data as the new oil. Well for it's explanation Now we are going to compare Data Vs Oil Data is an essential resource that powers the information economy in much the way that oil has fueled the industrial economy. Once upon a time, the wealthiest were those with most natural resources, now it’s knowledge economy, where the more you know is proportional to more data that you have. Information can be extracted from data just as energy can be extracted from oil. Traditional Oil powered the transportation era, in the same way that Data as the new oil is also powering the emerging transportation op...
1 comment
Read more

Ensemble Methods detailed explanation

One of the major tasks of machine learning algorithms is to construct a fair model from a dataset. The process of generating models from data is called learning or training and the learned model can be called as hypothesis or learner. The learning algorithms which construct a set of classifiers and then classify new data points by taking a choice of their predictions are known as Ensemble methods.In Other words we can say " Ensemble methods is a machine learning technique that combines several base models in order to produce one optimal predictive model." Why Use Ensemble Methods?? The learning algorithms which output only a single hypothesis tends to suffer from basically three issues. These issues are the statistical problem, the computational problem and the representation problem which can be partly overcome by applying ensemble methods.The learning algorithm which suffers from the statistical problem is said to have high variance. The algorithm which exhibits the co...
Post a Comment
Read more

Future of Data Science

It is rightly said that Data Scientists would be shaping the future of the businesses in the years to come. And trust me they are already on their path to do so. Over the years, data is constantly being generated and collected as well. Now, the field of data sciences has put this humongous pile of data to good use. Now, data can be collected, processed, analyzed and converted into a highly useful piece of information that would benefit the businesses with better and well-informed decision-making capability. "Data is a Precious Thing and will Last Longer than the Systems themselves." Also, Vinod Khosla, an American Billionaire Businessman and Co-founder of Sun Microsystems declared – "In the next 10 years, Data Science and Software will do more for Medicines than all of the Biological Sciences together." By the above two statements, it is clear that data proliferation will never end and because of that, the use of data related technologies like Data Science and Big D...
1 comment
Read more