In this session, let's understand the concept of central tendency and dispassion whenever you are presented
with any data set before you go on develop any statistical models, it is important to understand what
is going on in the data.
And the best way to understand the data is to use the concept of central tendency and dispersion.
So what is the central tendency in this push?
These are the techniques we use when it comes to understanding central tendency.
Dispersion tells me the extent of variation that is there in my process.
This tells about what is going on in my process, what is there in my dataset from the perspective of
the midpoint.
OK.
So you have a central tendency.
I mean, how does Bush analyze the data from both the perspectives it will view very useful insights.
OK, so let's understand the central tendency first and then we will go to this Bush.
OK, central tendency measures like mean median mode.
You'll see that first arithmetic range or simply range is a variation measure.
OK, so let's say you have a data dataset, nine three one eight three six, meaning simply some of
this divided by count.
Right.
If I add all the six members, the count the study, I divided by six.
I find this is simply the arithmetic average.
Median, on the other hand, is the midpoint.
Midpoint of my data set after I arranged the data set in an ascending order.
So this is the data set.
I have nine three one eight three six.
I arranged this in ascending order, one three three six, eight, nine, three and six.
The ones I've highlighted in blue, they are the midpoint.
Right.
So the median is three plus six, divided by two and four point five.
Let's assume for a moment, OK, six is not there.
What will be the median?
The median will be three.
Right, so you add and divide by two one leave and you have two data points as points, right?
If six is not there, there are only five data points and the midpoint is three.
We will go for the middle point.
OK, unmoored more than simply the frequently occurring number modestly and ranges maximum minus minimum
that is there in my data set.
OK, so I mean median.
What are the measures of central tendency that gives information about what is there in my dataset from
the midpoint perspective?
OK, now let's understand.
Standard Deviation already introduced a measure of variation that is range ranges, maximum minhas meaning
minimum standard deviation is the extent of variation that is there in my dataset from the.
Average.
OK, so the average one, two, three, four, five.
This is my dataset and three is my average.
I mentioned the extent of variation from three.
OK, then I squared it divided by nine minus one, and then I take a square root.
OK, this is the sum of the square of difference.
And then I submit count minus one is four, so 10 divided by four is two point five.
And the square root of this is one point fifty eight.
So my standard deviation is one point five eight.
We can also take the square of standard deviation, which is variance.
OK, we'll tell the extent of variation that is there in my data or process.
OK.
Having seen the concept of central tendency and dispersion, let's now look at the types of distribution
that you will encounter, OK?
You will either encounter a symmetrical distribution or a unsymmetrical distribution, right in a symmetrical
distribution, which is also called as a normal distribution.
The valley of mean median and mode would be the same in a skewed distribution.
You can either have a positive skew on a negative skew.
These values won't be the same.
So how will you create a graph like this, we use a technique called frequency distribution.
Frequency distribution is nothing but a display of different frequencies of data that is there in my
dataset.
OK, if you see this is the mark obtained by different students.
Nine students have got two marks for students, about one mark, six students have got three months,
so on and so forth.
If I plotted this graphically, it is known as the frequency distribution.
It tells me whether there is any skew that is there in my data set or not.
OK, so this understanding is also important.
OK, now we have understood the concept of distribution.
Now let's take a simple exercise, OK?
I have two frequency distributions.
I also have their averages and standard deviation.
These is the marks obtained by students in two different groups.
OK, this is group's performance.
This is Group B's performance.
Can you tell me which group is better and why?
Take a moment.
If you really see.
Group A is better because the standard deviation is lower when the standard deviation is lawyer, it
means my variation is lower.
Y variation has to be lower when variation is low.
My predictability for future from the current data set is higher.
When the variation is high in my predictability is obviously lower.
Right.
So from that perspective, it is important to understand the concept of mean versus standard English.
OK, let's look at one more example.
In this example, I have again a similar ESCOs scenario, meaning eighty five year, meaning that standard
deviation of seven standard deviation is 50.
Which one is better on one?
If you really see in this scenario also.
Team's performance, that is, this team's performance is better because the variation is low, OK,
and the average is also higher, right?
Normally in a test, you want more students to score higher marks, like look at these extreme data
points.
Look at the skew.
Right, which means that a variation is higher, that means more predictability for future will be lower.
Are you are you understanding the concept of standard deviation was as me?
OK, now let's see one more example.
I have four shooters, OK?
You have to tell me which order is the best.
OK, I think you all can guess that this shooter is the best.
Right.
And of the remaining three shooters who can actually become the best shooter, right.
He's the best shooter.
So I have three shooters now of the three shooters, which shooter can become the best shooter?
Right.
Ritual can perform like this.
You have one, two, three choices, these take a moment.
He said this, I think this is ruled out right, this shooter is all over the place.
This shooter is closer to the target, this shooter is away from the target, but the variation is low.
In my opinion, this shooter can become a very good shooter, much like this shooter.
OK, it could be that this shooter is probably not holding the gun properly or holding the gun at an
angle or not aiming correctly.
OK, all that this person has to be taught is to invent.
This person that is a Fashoda can actually do a good job if he's taught how to aim correctly.
OK, only a minor modification is needed in shooter one.
Shooter two and three will probably require more effort, more effort.
Only then they can become a shooter.
So shooter one can actually go all the way to the top just like the shooter.
Right.
So what is the concept we are trying to explain here in this case, precision versus accuracy, that
is a game mean.
What's the standard deviation in this case?
In this case, precision and accuracy?
Both are high, in this case, precision, accuracy, both are bad.
In this case, precision is lower.
Accuracy is fairly high.
In this case, precision is very good, but accuracy is low.
We actually want both precision and accuracy in our dataset.
You understand the concept of central tendency and dispositional.
OK.