Descriptive Statistics-03 : Measure Of Shape Or Frequency Distribution : Skewness | Kurtosis

Hi all welcome back. So today we are going to see different measure of shape or distribution of our data that is about skewness or Kurtis. So before that let's understand the term distribution, so it tells you, uh, what are all possible values? You have for a given variable in your data set, and how often they occur the frequency.

And these two together gives you the shape of the distribution by shape of the distribution. I mean, you know whether it's a symmetric uniform bimodal with two peaks, or they. Are skewed left or skewed right so like that we have different shapes of distribution. So now the skewness, uh. So in simple terms, it measures the lack of symmetry in your data distribution.

So how asymmetric your data distribution is so less symmetric. The data more will be the skewness. So if you remember the normal distribution is completely symmetric. So there the skewness is zero and for any kind of symmetrical data, uh, the skewness will be more or less close to zero. So now we know zero skewness. Then we have positive skewness and negative skewness so let's understand so now the positive skewness, uh, here, most of the value seems to be clustered around left side of the distribution. You can see in the graph and mean and median are greater than the mode on the x-axis.

You can see and contrary to this in the negative skewness. We have most of the values are clustered around right side of the distribution and mean and median are less than the more the most frequent value of the distribution. So.

Going forward so what value or range of these units is considered to be significant or notable. So here we have general rule of thumb. So if skewness is less than uh, minus one or greater than one, we say, it's, highly skewed distribution. And if uh it's in between minus one and minus point, five or between point, five and one, we say, it's, moderately skewed. And if is in between minus 0.5 to 0.5, we say, it's approximately symmetric, you know, more or less close to normal distribution. So now the Kurdish is.

So what does it tell us? So it measures whether the data distribution is heavy tailed or light tail. So when I say, you know higher Kurtis, so it means heavier the tail of a data distribution is, or you can say more the outliers we have there. So now let's understand when we say, you know, zero, Kurtis or positive or negative cutters.

So zero cartoons is also known as leptokurtic. And it looks similar to the normal distribution curve for the bell shaped curve. And you can say that probability of. Having outliers or extreme values is more or less close to zero. Then we have positive vertices also known as leptokurtic. And we see longer distribution here.

You can see the red dotted line. It shows a sharper peak and heavier tails at both ends. So heavier tails mean more outliers. Then we have negative Kurtis also known as platykurtic. And it shows a shorter distribution again. I see the red dotted line it's showing flatter peak and thinner tails. So thinner tails means less outliers.

So now, if I. Ask you what value of Kurtis is considered to be, you know, significant or notable. Then keeping this in mind that higher Kurtis, you know, more outliers in data.

You know, we already, uh saw the answers, uh in previous slide. So you see that for leptokurtic, we have zero cortices for lento, positive, Kurtis, Kurtis greater than three. And for platykertic, we have less than three.

So yes. Okay. So now a very important point, uh, when is Kurtis useful, only when it's used in conjunction with standard. Deviation because it's possible that our variable, you know, it's showing high courtesies, but the overall standard deviation is quite low and vice versa, showing low cortisol. But the standard deviation is high, which is bad. So keep this in mind. And so now we are finally a question, I leave this up to you so does sample size have an impact on skewness or Kurtis.

So you can think around. So yeah, that's all in this session, uh. Thank you so much for your time and see you soon until then take care enjoy. Bye.