 Hi everyone. It's MJ and I got asked this question. What is the difference between a statistic and a parameter? And this is a very easy question to answer if we look at the big picture of statistics We can see this is where our statistic is and this is where our parameters So we can see that they are different things, but I'm gonna explain the big picture I'm gonna see why it is sometimes confusing if we look at the big picture of statistics We know that what we're trying to do is get some information from data using mathematics We use some mathematical processes and we get some information from data Now the information that we're after is the distribution and the parameters of this thing called the random variable The random variable is the heart of statistics and why it is the heart is because it is the thing that generates the data in the first place And once we know the information about the random variable, in this case it's distribution as parameters We can use this information to answer questions and optimize processes in a whole wide variety of fields So it's a very very good thing to do So let's get into it. What exactly is a statistic? In a nutshell, a statistic is something that we use to estimate what the parameters are going to be And normally we're using this the subject here, point estimation is when we use the final result of a statistic And we say okay we're gonna use this to estimate our parameter But let's get a little bit deeper into it Let's say for instance that we have our random variable Random variable we can sometimes denote by capital letter X And let's say this random variable is normally distributed Once we know what the distribution is we know what parameters we're looking for In this case of the normal distribution it has the parameters mu and sigma squared Remember if the random variable was let's say the Poisson distribution Then we'd be looking for a parameter known as lambda But don't worry about that for now, we're looking at the normal distribution which has got two parameters Mu and sigma squared Okay now we know from normal distributions that the expected value of x is going to be equal to mu And the variance of our random variable when it's a normal distribution is equal to sigma squared Okay that is stuff that we know from just our studying of probability distributions So these things here just to say it again Mu and sigma squared these are our parameters Okay and these are unknown values that we're trying to figure out Now what can random variables do? Random variables can generate data So let's say our random variable generates some data And we normally denote the data by the lowercase x We have x1, we have x2, we have x3 These are data points of our random variable And together we can refer to them as a random sample or we use the notation x underline So x underline is going to be our random sample or it is a group of observations And this is where things get interesting because our statistic Okay is a mathematical function of the random sample Or states in more mathematically a statistic is given by this Where g is just representing that we're doing a function Now one of the most famous statistics of all time is something known as x bar Because what x bar is it is the sum of the observations Divided by the number of observations And this x bar is also known as the sample mean Now hold on, sample mean and this thing over here which is known as the mean And this is where we can start using statistics to give us information about the parameters Because what we're going to say is hold on, why don't we equate the sample mean to the parameter So here we have our statistic, here we have our parameter And we say that we are going to use our statistic to estimate what our parameter is going to be Where things start to get interesting is that this statistic over here Because it's made up of a random sample it is in its own right a random variable And because it is a random variable we know from our big picture That it too is going to have its own set of parameters and its own set of distributions And this is why some people get a little bit confused with statistics Because now we have a random variable in the case of a statistic That has its own set of parameters and its own distribution Now what are the parameters and distribution of a statistic? Fortunately there is a very big discovery in statistics something known as the central limit theorem Which comes in and helps us say what this distribution and what this parameter is going to be Now why we care about that is because let's say we just want to say Okay give me a single point estimate of what mu is We just calculate this value here and we say okay let's say we had 6, 7, 8 We go 6 plus 7 plus 8 divided by 3 and we can say okay cool 7 is our estimate for the parameter You could do that, you could do that But as soon as you start taking into consideration that the statistic is a random variable It has its distribution, it has parameters, it has its own variance You start using the central limit theorem You can start creating something known as confidence intervals And a confidence interval wouldn't be saying okay this is the single value You say that the parameter is going to be between two values And you give it a set of confidence saying at 95% But look we are getting a little bit ahead of ourselves But that's where you'll see confidence intervals start coming in When we start using the central limit theorem Which is giving us information about the parameters and distributions of the statistic So this is a lot of information to process all at once If you are a little bit confused watch the video again But the whole idea in statistics is that we have some data We want information from that data And the information we want is the parameters and distributions Of this thing called the random variable Because with it we can answer questions and we can optimize processes And yes we start off with simple algebra And we start getting a little bit more complicated When we start introducing calculus later on in the course But if statistics is something that interests you I do have a course on Udemy called actuarial statistics So just search Udemy for actuarial statistics Or you can go visit my online school course statistics by MJ And learn a lot more about this beautiful subject Which in my opinion is one of the most important subjects of the modern age But if you've got any questions feel free to let me know in the comment section below And I'll provide also links in the description so check that out Thanks guys, keep well, cheers