In this video, we will discuss descriptive numerical measures which describe the center of the data.
There are four values that they know decentered mean median Moore and mid-range.
If you are aware about this, you can skip the lecture else, let us discuss them one by one.
First is the also called average, it is obtained by adding all the values and then dividing by the
number of values.
The definition is pretty simple, but not these two delusions.
One is population me and the other is Tamplin.
If you want to find out the average height of, say, a hundred thousand people and you collect height
of a hundred thousand people and find average, that is population mean.
But if you think that this would be a difficult task and you collect it of only a hundred people assemble
and find the average that averages sample mean.
So population mean is denoted by Mbewe, the symbolism example, meaning is denoted by X Bar.
Let's look at an example.
Here are five students and their height.
What is the meaning of their right to be at the height and divided by five?
We get a twenty four divided by five, which comes out to one sixty four point eight.
So if the glass contained only five students, this will be the population mean, but if the glass contained
50 students and we were using the word of five students to calculate the mean, then this will be the
sample mean because this is a sample of five students out of the 50 student, depending on what mean
you are representing, you'll use the symbol here.
If it is population mean, then you'll write music to 160 420.
If it is sample when you write X bar is equal to one sixty four point eight.
Next comes median.
Median is the middle term when you order the data in increasing or decreasing order.
So first step is to order the data and then we will find the middle.
If the number of observations are ordered, then there will be a single random.
And that would be odd million, but if the number of observations are even, then there will be two
values in the middle.
In that case, we will take average of the two middle values.
Let's see an example again for the state of you'll find the median age.
So first we order these in ascending order.
And next, we find the middle value, which is the third value here, which comes out to 168.
Suppose we have another student.
Who has a height of 170 centimeters?
That value will come a default position, in that case, there will be two values in the middle, 160
and 170.
There will have to average these two values to give the median, so the median in that case will be
160 plus 170 by two, which will be 169 centimeters.
Next is more.
More value is the value which is occurring maximum number of times in the data.
So if you consider probability, more value has the maximum probability of occurrence, not depending
on the number of moles that the data has, it is given different names.
If data has to modes, it is bimodal.
If more than two modes, then it is multimodal or if no value is repeated and frequent is one for each
value.
Data has no more.
Let's see an example.
For this data, what is the mood hide?
So since 168 comes to times and every other value is coming only once.
168 is the here, if you go to the other data that we had when we calculated median, there is no repetition
of any height.
So this data has no more nexus, mid-range marriages.
Very simple.
You just find the average of largest and smallest values of your data to, for example, have the tallest
one is 182 and shortages 155.
Therefore, mid-range will be 155 plus 182 divided by two, which comes out to one sixty eight point
five.
So now we know the definitions of these measures of senator.
Now, let us compare them, if you remember, we are using the image of a histogram and we have symmetric
data like this, usually the mean median and mode will be identical.
But if the data is skewed, like in the two images after this one, the three values will be different.
Men will be highly influenced by the outliers here.
Million will still be at the center.
More will know the value with highest frequency.
So which one stays relevant for us depends on the data in case we have outliers.
We should either remove the outliers and then find something else, mediant would be our preferred measure
of center over me.
One advantage of Maude is that it can be concluded for qualitative, but also.
So, for example, if we have categories like north, east, west, south, and we want to find out
which category has the highest number of customers.
We just find the mode categories, so we assign the number of customers to each category and then the
more will be the category which has the maximum number of customers.
This is a qualitative data that it has categories and numbers assigned to it.
More can be found out for such data mean and median cannot be found out for such data, that is, you
cannot have a mean of North-Western told.
Also, if you are interested to know the probability of occurrence, Morde is still denoting the value
which has the highest probability of occurrence.
So these are the measures of center in the next video, we will discuss the measures of dispersion.