Hello everyone, welcome back to a new video.
Today's video is a continuation of the statistics video.
In the first video, we saw what we will study in statistics,
M3 that is mean, median and mod.
We learned about them, what are they, what type of data is
it, grouped, ungrouped.
And then in the next video, we found out the mean, median
and mod of ungrouped data.
I hope everyone has done it by now.
Next, we also learned about class interval.
Today, we will do for discrete frequency distribution.
That is the first case of grouped data, which is discrete
frequency distribution.
We will find out all three things, mean, median and mod.
So, let's see the first question of discrete.
How will be the question of discrete?
You will have a value of x, one column will be of x.
And the second one will be of frequency.
Frequency means, the number of times the value of x is
repeated, the frequency number will be given in front of it.
So, as soon as the question is, what is there in this? 8
and what is its frequency? 3.
That is, how will be your data?
Your data will be of this type.
That is, 8, 8 and 8.
3 times 8, 8, 8.
Then, 9 will be there.
You have 5 times.
9, 9, 9 and 9.
Not 5 times, it is 9.
Then, 10, 8 times.
So, 8 times you write 10.
8 times.
Then, 12, 7 times.
Before that, 11, 12 times.
Then, 12, 7 times.
And so on.
So, see this data, how much time you are taking to write.
And writing each and value, writing this data on a large
level becomes very tough.
That is why it is written in another form.
That is, in the form of frequency.
Frequency distribution.
So, how will be the table in discrete frequency
distribution?
You will be given values of x.
And in front of it, its corresponding frequency.
That is, how many times it is repeated in this data.
So, this is the question we have.
8, 9, 10, 11, 12, 13.
How many values do we have of x?
We have 6 values of x.
What do you have to do?
You have to find out the mean, median and mod.
So, first of all, let's move to the question.
How will we find out the mean of this data?
What is the mean?
Sum of all observations upon total number of observations.
Now, how do we find out the sum?
You will sum all the values of x.
And divide it by all the terms, all the number of
observations.
Now, look at this.
How many times is 8 coming? 3 times.
So, how many times do we have to add 8?
We have to add 8 3 times.
That is, 8 plus 8 plus 8.
Now, add 8 3 times.
8 plus 8 plus 8.
Or write it as 3 into 8.
Both are same.
So, what do you have to do? Multiply f and x.
Add 8 3 times.
Or multiply 8 by 3.
Answer would be the same.
Similarly, 9.
How many times is 9 repeated? 5 times.
Now, add 9 5 times.
9 plus 9 plus 9 plus 9 plus 9.
5 times.
Or write it as 5 into 9.
Both are same.
So, in this question, what do we do?
We make one more table.
What is the name of that column? f into x. That is, we
multiply f by x.
We multiply f by x.
So, 8 by 3 is 24.
9 by 5 is 45.
10 by 8 is 80.
12 by 11 is 132.
12 by 7 is 14.
And 1 is 84.
13 by 5 is 15.
And 1 is 565.
So, what is this?
This is the sum of the individual entries.
8 by 3 is 24.
9 by 5 is 45.
10 by 8 is 80.
11 by 12 is 132.
12 by 7 is 84.
13 by 5 is 65.
This is the sum of the individual entries.
So, what do we have to do to find the sum of all these
entries?
This is the sum of the individual entries.
So, what do we get in the end?
The sum of all these entries.
So, for the sum, the sign that you denote is the summation.
And what is the name of this column? fx.
So, you will find the summation fx.
What will it give you?
The sum of all these entries.
So, 24 plus 45 plus 80 plus 132 plus 84 plus 65.
So, if you sum all these entries, 9 plus 9 plus 2 is 11.
So, what do you get? 9 plus 9 is 18.
18 plus 2 is 20.
Then, 2 plus 2 is 4.
4 plus 4 is 8.
8 plus 8 is 16.
16 plus 8 is 24.
24 plus 6 is 30.
30 plus 3 is 33.
3 plus 3 is 4.
4 plus 4 is 30.
So, you get the sum of all these entries.
Summation fx is equal to 430.
So, what is the sum of all the observations?
If we want to find the mean, we will denote the mean as x.
We will denote the mean as x.
So, the sum of all the observations is summation fx divided
by number of observations.
Now, how do we find the total number of observations?
Some students may say that
Ma'am, it is 6, so it is x.
So, the total number of observations is 6.
So, what will happen here?
I will say no.
It will not be 6 because we are repeating it.
We have to count that also.
The number of times 8 is repeated, 9 is repeated 5 times.
So, we have to count that also because that is also an
individual entry.
So, how do we find the total number of observations?
By adding all the frequencies.
By adding all the frequencies, the repetition will also be
added.
Everything will be added.
So, that will give us the total number of observations.
That is capital N.
What will be the value of capital N?
It is summation f which is total number of observations.
So, what is the formula for discrete?
This is for discrete frequency distribution.
For discrete data.
What is the total number of observations?
It is summation f.
So, here you have written summation f.
How will you find summation f?
By adding the column of f.
So, add 12, 8, 20, 20, 7, 3, 10, 30, 30, 10, 40.
Here you have the sum.
You have 40.
10, 20, 30, 40.
You have 40.
Summation f.
So, its value is 40.
Now, substitute the values.
It is equal to 430 divided by 40.
Cancel.
Now, if we divide it by 4, what will we get? 1, 1, and then
1, 0.
Because it does not come.
30.
If we do 30, then 7 comes, 28, then 20 comes, 5.
So, what do you have?
The mean of this data is 10.75.
I hope it is clear till now.
How to find the mean in discrete frequency? Same formula.
Sum divided by total number of observations.
Total number of observations will come from frequency.
And total sum will come from the column of f into x.
Simple.
The next thing we will do is mod.
How to find mod?
Mod is the value which is repeated the most in the data.
The highest value which is repeated the most in the data is
called mod.
So, which value will be repeated the most? This can be
found from the frequency.
What is the highest frequency? 11, which is 12.
12 is the highest frequency.
What is the corresponding data? x is equal to 11.
So, 11 comes. of this data that is observation with highest
frequency, observation with highest frequency that will be
your mod of this data now it is main and mod third one is
median now we will find out median erase this it is main
and mod next is third
is median in median also it is same you have to see first
whether your data is arranged
first thing for data is for median you have to see whether
your data is arranged data is already sorted that is
highest, lowest then highest and increasing order in
ascending order your data is arranged now what you have to
do suppose it is not arranged
then you solve for next for median we have to find out fx
but for median we have to find out new column that is cf
now what is cf what is full form of cf full form of cf is
cumulative frequency cumulative frequency what is
cumulative frequency for median
we need middle term middle term will lie on which position
for that we have to see cumulative frequency how to find
out cf 8 is repeated 3 times so first, second and third
place so it will remain as it is second frequency
observation is done till 8 then
we have 9 9 is repeated 5 times so which position will 9
take 3rd, 4th, 5th, 6th, 7th and 8th so it is 5 so
positions till 8 positions till 8 are filled by 9 and
before that 3 was filled by 8 so we have to add
corresponding frequencies in previous cf
suppose it is 3 so to find out cf 5 plus 3 that is 8 5 plus
3 that is 8 8 plus 8 that is 16 12 plus 12 that is 28 28
plus 28 that is 35 28 plus 28 that is 35 35 plus 35 that is
40 35 plus 35 that is 40 means you have 8 till 3 4th, 5th,
6th, 7th, 8th 9
to 16 10 to 16 17 to 28 11 to 28 29 to 29 30 to 35 35 to 36
36, 37, 38, 39 and 40 30 to 36, 37, 38, 39 and 40 30
cumulative frequency last position is last position total
number of observations is summation f that is capital N in
this question we had
40 last value of cf is 40 means we are doing right we have
calculated cf right now we have cf total number of terms is
40 and what we need first we have to check we will do same
formula you must have seen this formula for even we have to
take mean for
odd we have to take observation so what we will do we have
even for even we can divide by 2 we will take this
observation then second one is 40 by 2 plus 1th observation
and we will divide by 2 40 by 2 is 20th observation plus
21st observation divided
by 2 so what we have this is the position what is the
location what is the value we have to find out that is why
we have taken cf how will we know that 20th 16th 17th 11 11
20th 21st 20th 21st 11 11 11 by 2 that is 22 by 2 which is
again 11 only 11 is
the median of this data
I hope you have understood mean, median and odd for
discrete frequency distribution ungrouped data was the
easiest little bit tough
I will not say more tough like finding cf in median and for
mean you have to find fx column mod is same highest
repeating term is highest frequency so these three are for
discrete frequency distribution then we will continue in
next class class interval
till then you practice these two ungrouped data and
discrete frequency distribution meet you in the next video
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