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

Math Skills required for Data Science Aspirants

The knowledge of this essential math is particularly important for newcomers arriving at data science from other professions, Specially whosoever wanted to transit their career in to Data Science field (Aspirant). Because mathematics is backbone of Data science , you must have knowledge to deal with data, behind any algorithm mathematics plays an important role. Here am going to iclude some of the topics which is Important if you dont have maths background.  1. Statistics and Probability 2. Calculus (Multivariable) 3. Linear Algebra 4.  Methods for Optimization 5. Numerical Analysis 1. Statistics and Probability Statistics and Probability is used for visualization of features, data preprocessing, feature transformation, data imputation, dimensionality reduction, feature engineering, model evaluation, etc. Here are the topics you need to be familiar with: Mean, Median, Mode, Standard deviation/variance, Correlation coefficient and the covariance matrix, Probability distribution...
Post a Comment
Read more

Data Analytics Interview Questions - Part 1

Q1. Python or R – Which one would you prefer for text analytics? We will prefer Python because of the following reasons: Python  would be the best option because it has Pandas library that provides easy to use data structures and high-performance data analysis tools. R  is more suitable for machine learning than just text analysis. Python performs faster for all types of text analytics. Q2. How does data cleaning plays a vital role in the analysis? Data cleaning can help in analysis because: Cleaning data from multiple sources helps to transform it into a format that data analysts or data scientists can work with. Data Cleaning helps to increase the accuracy of the model in machine learning. It is a cumbersome process because as the number of data sources increases, the time taken to clean the data increases exponentially due to the number of sources and the volume of data generated by these sources. It might take up to 80% of the time for just c...
Post a Comment
Read more

Data Science Interview Questions -Part 2

1) What are the differences between supervised and unsupervised learning? Supervised Learning Unsupervised Learning Uses known and labeled data as input Supervised learning has a feedback mechanism  Most commonly used supervised learning algorithms are decision trees, logistic regression, and support vector machine Uses unlabeled data as input Unsupervised learning has no feedback mechanism  Most commonly used unsupervised learning algorithms are k-means clustering, hierarchical clustering, and apriori algorithm 2) How is logistic regression done? Logistic regression measures the relationship between the dependent variable (our label of what we want to predict) and one or more independent variables (our features) by estimating probability using its underlying logistic function (sigmoid). The image shown below depicts how logistic regression works: The formula and graph for the sigmoid function is as shown: 3) Explain the steps in making a deci...
Post a Comment
Read more