Hello everyone, welcome back to another video.
Today's video is a continuation of the last video of
statistics.
In statistics, what we had studied in the last video, we
had studied the main terms, what is mean, median, and mod.
We had taken an overview of them broadly.
We had classified the data, that what type of data will be
there.
We had studied three types, ungrouped, grouped and
ungrouped.
And then further two categories of grouped data, that was
discrete and continuous frequency distribution.
And then we had studied the definition of frequency.
So, in today's class, we will study the first type of data,
that was for ungrouped data.
For ungrouped data, we will find out all three types, that
is mean, median, and mod.
We will find out what is mean, median, and mod.
So, let us see the example of ungrouped data, that how will
be given to us. See this, you have this, ungrouped data.
Can you see? Whose values are visible only?
X's.
Suppose you have marks, marks out of maximum, what is
visible? 30.
So, marks out of 30 are visible. So, let us see that.
The first thing, the easiest thing that we learn, that is,
first mean.
There are only three easy things, but first of all, let us
move towards mean.
How will we find out mean? The formula for mean was, that
you sum up all the observations, and divide it by, whatever
is the total number of terms. So, first of all, we have to
count, that how many terms are there.
Count.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
The total number of terms we have is 10.
So, capital N is written as 10, which is total number of
observations. Total number of observations.
It is 10.
Now, for mean, we have to find out the sum of all.
So, you find out the sum of all.
What will be the mean?
Sum upon the number of observations.
So, if you do the sum, then what will you do? 15 plus 8
plus 10 plus up to, last 25 plus 30.
Do the sum of all these.
Divide it by N.
That is 10.
So, find out the sum quickly.
Find out the sum.
I know the sum.
Let us see from here.
What is the sum of this? 174.
Check it once.
If there is something else, check it.
But, write the sum here.
And, what will you write in divide? N.
Total number of observations.
That is 10.
Now, if you divide by 10, what will you get? 17.4.
17.4. So, what is the mean of this data? 17.4.
Mean is also an average.
If you see all these numbers, 8 is the start, 8 is the end,
10, 11, and the last one is 30.
So, the average of this data is 17.4.
Average.
Means, all the values around it, big values will be in
front of it, and small values will be behind it. That is it.
So, what is the mean of this data? You have learnt the mean.
The simplest one is mean.
The second one that you are learning, I will tell you the
mod.
For median, it will take a big page.
So, we will start with a fresh page.
So, to tell you the mod, what was the mod?
Whichever term is coming out the most in the data.
Now, which term is coming out the most in the data?
See, 15.
It is coming out once, it is coming out twice.
So, 15 is coming out twice.
8 is coming out once, 10 is coming out once, 11 is coming
out once.
Rest all are coming out once.
There is only one number 15, which is coming out twice.
Rest all are coming out once.
So, who is repeating the most number? 15 is repeating.
So, 15 is the mod.
What is the mod?
Whichever number is coming out the most in the data, that
will be your mod.
So, I have done this.
If I have done this, then I am erasing it.
I hope you have taken a screenshot or written it.
Next, what we have to do is that is median.
The third wheel of M3, which is median.
How will you find out the median?
For median, what was the first point I told you?
What will you do first?
You will sort the data.
That is, you will arrange.
Either you will do it in ascending or in descending.
So, we will arrange the data in ascending order.
Ascending means, small, then big, then bigger than that,
then bigger than all.
So, what is the smallest value in this?
The smallest value is 8.
Then, what do you have? 10.
Then, 11.
Then, you have 15.
You wrote it twice.
Then, you have 18.
You also wrote 18.
Then, you have 20, 22, 25, 30.
This is sorted.
Okay? 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
What are the 10 terms of 10?
You wrote it.
In which order?
In ascending order.
Okay? Now, after arranging in ascending order, you will see
its middle term.
How will you see its middle term?
You will see, 2 are subtracted from both sides.
This is subtracted from both sides.
Then, 10 is also subtracted from both sides.
10 is subtracted.
25 is subtracted from both sides.
11 is subtracted from both sides.
22 is subtracted.
15 is subtracted.
20 is subtracted.
The middle term is 15 and 18.
15 and 18 are the remaining two terms in the middle.
You could have removed 15 and 18 as well if there was any
other term remaining in the middle.
But there will be no other term remaining in the middle,
not a single term.
Because this is an even number of terms, 10 is even.
So, there will always be two terms remaining in the middle
when you have data which is of even number of observations.
So, write down the case of median when you have the value
of n as even.
So, what will happen for even?
There will be two terms remaining.
And what will you have to take for those two terms?
You will have to take mean or average for those two terms.
So, what are the two terms?
Add both 13 and 18.
And divide by 2 for the two terms you have added.
What will be the median?
So, write down the value of median.
What will you get? 5 plus 8 is 13.
And 1 is 33.
33 by 2.
If you solve this, what will you get? 1, 1, 6, 16.5.
What will you get for 16.5?
You will get the median, the middle value.
You cannot see it in this data.
But, what is it?
The point in the middle of this will be 16.5.
Okay? So, next you will get the median, 16.5.
What was the mean?
You got the mean.
17.4, I guess.
And what was the mod value?
You got 15.
So, all these terms are not the same.
But, they are close.
All the observations were from 8 to 30.
But, you got some middle values.
You can study and analyze the data further.
Okay? So, you have learnt the mean and median.
Now, in the ungrouped data, what will you do?
In the ungrouped data, the mean and mod will be on the same
base.
That is, take out the sum.
For the mean, divide by n.
The mod will also be the same.
If you are repeating it many times, take it out and take it
in the mod.
Now, what will be the difference?
In the median.
Why will it be in the median?
Because, there can be two types of data in the median.
One can be either even or odd.
So, let's write the formula for the median.
Generalized.
That is, median.
There will be two formulas for the median.
The first formula will be when the total number of
observations is even.
If it is even, then you will get two terms in the middle.
To find out those two terms, the formula is
N by 2.
Half it.
Find the observation.
N by 2.
by 2 plus 1.
That is n by 2 plus 1.
This is for the case when n is even.
For odd, we have not done any example.
So, let us see this example.
Let's suppose, we remove the last term.
This one, 30.
We have removed the 30 term.
When you remove the 30 term, then you have only 9 terms.
So, how will you remove 9?
First, you remove 8 from the starting.
Remove 25 from the last.
Remove 1 pair.
Remove 10 from the starting.
Remove 22 from the starting.
Remove 2nd pair.
Remove 11 from the starting.
Remove 20 from the starting.
Remove 15 from the starting.
Remove 18 from the starting.
So, in the middle, you will get only 1 term.
Whenever it is odd, that is 15.
So, what will you get?
Its median.
You will get 15.
For 15, your formula will be
First, it is odd.
We have to divide by 2.
So, let us make it even.
To make it even, we have to add 1 to it.
Even number is made.
Odd plus even.
Now, what to do?
Divide it by 2.
So, whatever observation will come, on this position, we
are looking for this position first.
Then, whatever value will be there on this position, you
will put it here.
Your median answer will come.
Let us do it once with the formula.
For the last question, we have 10 terms.
N is even.
So, what will you do for N is even?
What was for N is even?
For N is even, when we have N is even, we will get 2 terms.
Which one?
One is N by 2.
Find this term.
And, find the previous one.
So, N by 2.
That is 10 by 2.
5th term.
Find the 5th term.
1, 2, 3, 4, 5.
Which is the 5th term? 15.
Then, this is the 5th term.
And, what will be this?
That is the 6th term.
So, which is the 6th term?
This is the 5th.
So, this is the 6th.
18.
Now, what to do for these two?
Add and divide by 2.
So, add the 5th and 6th terms.
That is, you have 15 in the 5th term.
18 in the 6th term.
And, divide by 2.
This is what you had.
We had done that.
That was a small data.
So, we did it quickly.
But, if it is a big data, then what do we need?
We need a formula.
That formula is of your mean.
Where is it?
It is of median.
Here it is.
So, in median, you will have a problem that those two will
be different.
In which?
In ungrouped data.
And, mean will be same.
The formula of mean and mod will be same.
Whichever is repeated the most.
So, you have to practice this much.
You have to question on this.
On which?
You will get it in the discrete one.
To question in the description, you have to practice that.
Then, in the next video, we will meet you with group data.
Till then, keep learning and practicing.
I'll make sure to spread the word to all my knowns.