Hello everyone, welcome back to a new video.
The topic we are going to discuss in today's video is
Statistics.
And we will do data interpretation on the basis of this in
the next video.
What statistics we will do now is your basic level
statistics.
Which you must have learned in school till 10th, 11th.
We will do that type of statistics in today's class.
When we hear the word statistics, what do we study in
statistics?
First of all, it is important to know that statistics is a
branch of mathematics.
In which we study the data and then analyze it.
We study the data and then analyze it.
And then whatever interpretation we have to get, we get
that data.
So in today's class, we will be given the same data.
We have to find three things on the basis of that.
You must have heard those three things.
Whatever big data we have, what do we find out?
We measure the central tendency.
Because we have big data, it will take time to study it.
The more entries, the more time it will take to study
individual entries.
So instead of not studying those individual entries,
What we do is, we bring such a thing, such a value.
With which we can do what to the whole data?
We can depict it or we can analyze it a little bit.
For example, what happened?
Like your class students.
Everyone has gone to school, they have gone to tuitions.
Or whatever India's level exams, competitive exams.
What do you get?
You get marks in every subject.
Then you get the average of all the subjects that you have
got.
Then you get the percentage.
And then you get the rank.
First rank, second rank.
Or whatever your percentile is, you get that.
So we cannot read or study the data of each and every
student.
What do we do?
We take out some central tendencies of the whole data.
Because of which we can depict or analyze the data.
This is our statistics.
In statistics, the three central tendencies that I am
talking about.
With which we can study the data further.
All of you must have read those three.
That is Mean, Median and Mod.
M3 is Mean, Median.
Let us first understand what is Mean, Median and Mod of any
data.
Mean is nothing.
It is the same fancy word for average.
You have read the average chapter.
What was average?
Sum of all the observations.
All the entries divided by number of observations.
This was your mean.
We have given it a fancy name.
Sorry, average.
We have given it a fancy name.
That is mean.
Mean is nothing.
It is just an average.
What is average?
Arithmetic mean.
The simplest formula of mean is
Sum of all the observations.
Divided by total number of observations.
This will give us the average of the whole data.
Like you calculate the average run rate of a cricketer.
How much average per over run rate is going on.
How much is needed.
That is mean or average.
The formula of mean is
Sum of all the data entries.
Add up all the data entries.
Divide it by total number of observations.
10 things are added up to 10 things.
Divide it by 10.
The second central tendency is
First is mean.
Second is median.
Median is your mid value.
Mid value is your mid term.
Whatever data you get will be your median.
There is a problem in mid term.
What is the problem?
If someone has written marks of 1 to 10.
We need median.
So the values in the middle should be taken as 1 to 10.
Means 5th or 6th roll number.
Or the median of marks should be taken.
This is the problem.
What will we take as median?
We will not take median of number.
First of all median will have a property.
That data will be sorted.
Sorted means either write in ascending order or in
descending order.
This is your sorted data.
Which is given in any particular order.
Otherwise if median.
If every person will take it separately.
Then that entries can be written in any order from random
order.
Then what will be the value of median?
Then median value will differ from person to person.
Which is not right.
Because someone is getting the answer in maths.
So the same answer should be given by everyone.
It should not be different.
But if person A has written roll number 1 to 10.
And someone has written in random order.
Sometimes 2 or 5.
The one who was getting roll number.
He noted down the marks.
So his median or mid value will be different.
And the middle value of the previous person will be
different.
So to solve this confusion.
What will we have to do for median?
First of all we have to arrange the data.
Arrange the data first.
And then you take out the middle term.
So this is the median.
Now what will be the formula of median?
That how many number of terms it will depend on?
What will happen if it is even?
What will happen if it is odd terms?
For example if it is even number.
You have 3.
A, B, C.
So you can see the mid value of this.
B is in the middle.
So that is the middle value.
So you got the median.
But if you had 4 like this.
Then A, B, C, D.
It becomes 4.
Even number of terms becomes 4.
Now how will you find the median?
Because there are 2 values in between.
So whenever there are 2 values in between.
That is even number of terms.
So we will take the mean.
Or we will take the average.
We will do this later.
Now understand the definition of median.
Which is the middle observation of the arranged data.
Sorted data.
That will be the median value.
So you understood the two.
You understood the mean and median.
The third one is the mod.
What is mod?
Now you have given the marks of the entire class.
So there will be a particular mark.
Like 10 marks.
10 marks for one person.
For Shikha.
For Rohit.
For Surya.
Most of the students got 10 marks.
So we need the value of the data.
Which most of the students have.
Means.
Tell me the marks of the class.
Which most of the students have.
Like a class test.
Someone got highest.
Someone got lowest.
Someone got average.
But there will be a particular mark.
Which most of the students have.
Like if easy paper is given.
Then how many marks will most of the students have?
Full marks can be given.
Highest marks can be given.
If it is the easiest paper for most of the students.
And if it is a tough paper.
Then highest marks will be given.
But in tough paper.
Students will have more marks.
So their marks will be 0, 1, 2.
So the number which is coming most of the times.
And is getting repeated.
That is your mark.
Which is the maximum number of times.
Which is getting repeated.
In the data.
The number repeating maximum number of times.
Which is coming in the data.
That is the value of your mark.
So in all three, we got to know.
What is mean?
What is median?
What is mod?
Now we will see from the question.
How to calculate mean, median and mod? Before calculating
that. There are some important things that we need to know.
The first important thing that you need to know is the name
that is repeated a lot, which is frequency.
What is frequency?
What is frequency and whose frequency is it?
We need to know this.
Everyone must have searched for this.
If someone has a particular type of paper, he will
definitely search for it.
Frequently asked questions in UPSC, frequently asked
questions in SSC mock test or interview, frequently asked
questions in CAT or CAT interview, are the most frequently
asked questions.
The most frequently asked questions, which are repeated
every year or two, are frequently asked questions.
Similarly, the frequency denotes the number of times a data
value is repeating itself.
For example, I said that 10 marks were given to most of the
students.
How many marks were given to those 10 students?
Suppose, 5 students have 10 marks.
So, how many times is the frequency of 10 marks?
How many times is the frequency of 10 marks repeated?
If you make a list of those marks, how many times will 10
be repeated in the list? 10 marks are given to 10 students.
So, 10 marks will be repeated 10 times.
So, how many times is the frequency of 10 marks? 5 marks.
Sorry, how many times is the frequency of 10 marks repeated?
If 10 marks are repeated 5 times, then the frequency of 5
marks is 5.
For example, someone has 30 marks.
30 marks are given to 2 students.
So, what is the frequency of 30 marks? 2.
How many times is the frequency of a data value repeated?
The frequency is called the frequency.
The number of times a particular data is repeating or a
particular value or a particular entry is repeating.
So, what will be that frequency?
Number of times a value is occurring or repeating.
So, we have understood the definition of frequency.
Now, we will discuss the definition of data.
What are the forms of data?
Till now, I have been saying only one word.
Data, observations, values, elements.
I have been saying only these names.
But, how many forms of data will be given to us?
It will be given to us in three forms.
In statistics.
In statistics, what we are doing now, mean, median, and
mod, we will talk about three types of data.
The first one will be ungrouped data.
It is known by the name ungrouped.
What is ungrouped?
Ungrouped.
You are not grouping it.
You have scattered the numbers.
For example, there was a student and I am a teacher.
I am telling the student to take this answer sheet and tell
me the marks one by one.
Whatever question paper you are getting, you tell me the
roll number of that paper and the marks in front of it.
So, he will tell me the marks of each student in random
order.
Now, the marks are not sorted.
They are not sorted in increasing or decreasing.
The frequency is not given.
How many times is one thing repeated?
Nothing is given about it.
You are just given a line of marks.
Suppose, there are ten names.
The first five are marks.
The second six.
The third seven.
Eight, nine, ten.
Then, it is repeated.
Six, seven, five.
Eight, nine.
Then, eight, seven.
What is given in random order?
You got the list.
However, what is he doing?
However, what is this?
It is given in a list.
It is not sorted.
Nor is it grouped.
It is just given to you.
That this is a list of marks.
You write it.
So, what do we call this type of data?
Grouped data.
You will call it grouped data.
The second type of data.
The first type of data is grouped data.
The second type is ungrouped.
The second type is grouped data.
This is ungrouped.
It is not sorted.
You will see what is grouped data.
The data will be the same.
Suppose, this is the data you have.
Now, you make it presentable.
Now, it is not presentable.
We have just noted down the marks in a paper.
Now, we will write it in a presentable form.
How will we write it in a presentable form?
Now, see.
There will be marks from 1 to 10.
It was a test of 10.
So, the number can come from 0 to 10.
Suppose, we have this number.
So, the number can come from 10 to 9, 8, 7, 6, 5.
All these numbers are coming.
They are not coming below these numbers.
So, what will we do with grouped data?
Let us write 5.
First, 5 is coming.
Then, 6 marks are coming.
Then, 7 is coming.
Then, 8 is coming.
Then, 9 is coming.
And, 10 is coming.
All these 6 marks are being repeated.
None of these marks are outside the group.
Now, these are the marks.
What are these marks?
These are the marks.
Now, you have made a table of these marks.
You have written the marks.
Now, how many children do these marks belong to?
You have also written that in front of them.
That is, how many children do these marks belong to?
That means, how many times are they being repeated in this
list?
So, let us see 5.
How many times are 5 being repeated?
Once.
And, twice.
So, what will you write after 5? 2.
That means, there are 2 children whose marks are 5.
Now, how many marks are there for 6? 1.
What are the marks of 6? 2.
6 is also repeated twice.
So, what is the frequency of 6? 2.
Then, how many times is 7 repeated? 7 is repeated 3 times.
Once.
Twice.
Three times.
Once, twice, three times.
Now, how many marks are there for 8? 8 is also repeated 3
times.
Once.
Twice.
Once.
Twice.
Once.
Twice.
Once.
Twice.
How many marks are there for 9? 9 is repeated only once.
Once.
Twice.
You have only 9 marks of 2 children.
What are the marks of 10? 10 is repeated only once.
Only once.
10 is only repeated once.
What is done here?
You can write the data in this way.
This is rough data, ungrouped data, you have written it as
you found it.
And one more thing is that you have made it presentable.
If you want to give a list to principal sir, that so many
marks have been scored by students.
But how many marks have been scored by students, you tell
that in one column.
That two students have scored 5 marks, then two students
have scored 6 marks, 7 marks have been scored by 3
students, 8 marks have been scored by 4 students.
You have told this.
So, this number of students column, what it is telling is
that how many times a particular marks value is repeated.
And whose definition of repeat is this?
It is of frequency.
So, whose column is this?
It will automatically become frequency.
The number of students in the given column, what is it
telling us?
It is telling us the frequency of whose data?
Of this data.
What is this data?
Data of marks.
Now, we will denote the data of marks with X.
Because any data, we have written it as X.
Then what is written on its side?
We have written frequency.
So, what we will do is, we will make a table.
So, this is our example of grouped.
Now, this is a particular example of grouped, which is,
which form?
The first example of grouped is this discrete form.
Discrete means different, scattered, discrete.
So, discrete means these are different marks, 5, 6, 7, then
you have given their frequency.
One, your second part comes, which is, the second part of
your group comes, that is, continuous frequency
distribution.
What is the meaning of continuous frequency distribution?
That you have data, instead of discrete form, means,
instead of having different numbers. a a a a a a a a a a a
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