The Central Limit Theorem: Understanding its Importance and Visualization in Python

We have established a solid base with conditional probabilities now let's get into the central limit theorem or CLT what it is why it's important and how to visualize it in Python. Central limit theorem says that with a large enough collection of samples from the same population, the sample means will be normally distributed.

Note that this doesn't make any assumptions about the underlying distribution of the data. With a reasonably large sample of roughly 30 or more, this theorem will always ring true no matter what the population looks like. Central limit theorem matters because it promises our sampling mean distribution will be normal. Therefore, we can perform hypothesis tests more concretely.

We can assess the likelihood that a given mean came from a particular distribution and then based on this reject or fail to reject our hypothesis. This empowers all of the a/b testing you see in practice for this reason and our viewers love this topic so be sure to have a well thought out answer prepared. It's also worth mentioning that this is different than the law of large numbers.

The law of large numbers states that as the size of a sample has increased, the estimate of the sample mean will more accurately reflect the population mean. We see this here with the purple red and gold distributions representing small medium and large samples respectively. This is different from the central limit theorem that was easy to get mixed up in a high stress interview setting.

We can run a simulation in Python to get the following plot showing the roles of a normal six-sided die. In order to do this, we will utilize the numpy r + int function where we input the start and end number of values that we want to randomly generate along with the numpy mean function. The sample means don't look like much at first here but they slowly become more and more normal around the true mean of 3.5 thanks to the central limit theorem at work.

The simple matplotlib histogram shows only roles 1 through 100 but you can imagine how this would continue if we up the number of trials. Before we wrap up, let's cover list comprehension. List comprehension is a pretty cool Python trick that comes in handy for setting up these numpy simulations and certain coding interview questions as well.

Here, you see a snippet of some code that's designed to take in our list and square each value using list comprehension. This up by allowing you to execute your for loop and only one line giving us the same answer wrapping things up let's summarize what we learned. We talked about central limit theorem what it is and why it matters.

We touched on the law of large numbers, looked at a simulation of CLT in Python, and finally went over list comprehension. Remember, interviewers love central limit theorem and it's really fundamental to data science so was worth gaining a certain level of familiarity with the topic but enough on TLT for now let's get

"WEBVTTKind: captionsLanguage: enwe've established a solid base with conditional probabilities now let's get into the central limit theorem or CLT what it is why it's important and how to visualize it in Python central limit theorem says that with a large enough collection of samples from the same population the sample means will be normally distributed note that this doesn't make any assumptions about the underlying distribution of the data with a reasonably large sample of roughly 30 or more this theorem will always ring true no matter what the population looks like central limit theorem matters because it promises our sampling mean distribution will be normal therefore we can perform hypothesis tests more concretely we can assess the likelihood that a given mean came from a particular distribution and then based on this reject or fail to reject our hypothesis this empowers all of the a/b testing you see in practice for this reason and our viewers love this topic so be sure to have a well thought out answer prepared it's also worth mentioning that this is different than the law of large numbers the law of large numbers states that as the size of a sample has increased the estimate of the sample mean will more accurately reflect the population mean we see this here with the purple red and gold distributions representing small medium and large samples respectively this is different from the central limit theorem that was easy to get mixed up in a high stress interview setting we can run a simulation in Python to get the following plot showing the roles of a normal six-sided die in order to do this will utilize the numpy r + int function where we input the start and end number of values that we want to randomly generate along with the numpy mean function the sample means don't look like much at first here but they slowly become more and more normal around the true mean of 3.5 thanks to the central limit theorem at work the simple matplotlib histogram shows only roles 1 through 100 but you can imagine how this would continue if we up the number of trials before we wrap up let's cover list comprehension list comprehension is a pretty cool Python trick that comes in handy for setting up these numpy simulations and certain coding interview questions as well here you see a snippet of some code that's designed to take in our list and square each value list comprehension Titan's this up by allowing you to execute your for loop and only one line giving us the same answer wrapping things up let's summarize what we learned we talked about central limit theorem what it is and why it matters we touched on the law of large numbers looked at a simulation of CLT in Python and finally went over list comprehension remember interviewers love central limit theorem and it's really fundamental to data science so was worth gaining a certain level of familiarity with the topic but enough on TLT for now let's getwe've established a solid base with conditional probabilities now let's get into the central limit theorem or CLT what it is why it's important and how to visualize it in Python central limit theorem says that with a large enough collection of samples from the same population the sample means will be normally distributed note that this doesn't make any assumptions about the underlying distribution of the data with a reasonably large sample of roughly 30 or more this theorem will always ring true no matter what the population looks like central limit theorem matters because it promises our sampling mean distribution will be normal therefore we can perform hypothesis tests more concretely we can assess the likelihood that a given mean came from a particular distribution and then based on this reject or fail to reject our hypothesis this empowers all of the a/b testing you see in practice for this reason and our viewers love this topic so be sure to have a well thought out answer prepared it's also worth mentioning that this is different than the law of large numbers the law of large numbers states that as the size of a sample has increased the estimate of the sample mean will more accurately reflect the population mean we see this here with the purple red and gold distributions representing small medium and large samples respectively this is different from the central limit theorem that was easy to get mixed up in a high stress interview setting we can run a simulation in Python to get the following plot showing the roles of a normal six-sided die in order to do this will utilize the numpy r + int function where we input the start and end number of values that we want to randomly generate along with the numpy mean function the sample means don't look like much at first here but they slowly become more and more normal around the true mean of 3.5 thanks to the central limit theorem at work the simple matplotlib histogram shows only roles 1 through 100 but you can imagine how this would continue if we up the number of trials before we wrap up let's cover list comprehension list comprehension is a pretty cool Python trick that comes in handy for setting up these numpy simulations and certain coding interview questions as well here you see a snippet of some code that's designed to take in our list and square each value list comprehension Titan's this up by allowing you to execute your for loop and only one line giving us the same answer wrapping things up let's summarize what we learned we talked about central limit theorem what it is and why it matters we touched on the law of large numbers looked at a simulation of CLT in Python and finally went over list comprehension remember interviewers love central limit theorem and it's really fundamental to data science so was worth gaining a certain level of familiarity with the topic but enough on TLT for now let's get\n"