In this video, we will learn how to summarize data by creating a frequency distribution tables for
qualitative and quantitative data.
Then we will see how to convert these tables into backyards and how to construct Instagram's.
This is basically descriptive statistics where we describe the distribution of our data.
So let's start what is the frequency distribution?
Frequency distribution is listing down categories from our data and against each category.
We will write the number of elements or data points that belong to each category.
So suppose 420 students get admission into a college and you have to work, column one contains student
names and column two contains the branch of specialization of that student.
Such data is raw data, but when you take out these branches as categories and find out the number of
students that belong to each branch, you get a table like this.
This is called a frequency distribution.
Now, these numbers on the right are the frequency of occurrence of each branch in our raw data.
There is a term called relative frequency of a category which represents the contribution of that category
to the total.
That is mathematically it is frequency of that category divided by the sum of all frequencies.
So radiofrequency for biotechnology will be sixty, divided by 420.
Which comes out to be point one for which is nearly fourteen point two percent.
The same information can be depicted in the form of a graph called Bajak.
In a vertical backyard, the categories go on the horizontal axis and the frequency value is denoted
by the height of the vertical bars.
This is a fairly common chart and it's very easy to draw.
Judging that which is the most popular brands may have been difficult if we were looking at raw data,
but here we can easily see that more students go for electrical engineering, at least go for mathematics.
Earlier, we saw frequency distribution for quality, the greater knowledge frequency, distribution
for quantity, the reader quantitative data, we have to create the buckets first.
And when we create these buckets and assign the frequency of occurrence of values that belong to that
bucket, we get group data.
So suppose we have a list of students and their science marks, this is and group data, but when I
create category of marks such as zero to 35, 36 to 55 and so on, and find out the number of students
where scored Martin each category, I get this table and this table is group data.
And we will learn to do this using software like Oren Python, but for a small number of observations,
we can do it manually also.
So let's learn how to do it manually.
First, we have to decide the number of buckets, usually we keep it between five and 20.
Next, we decided last word, last word is decided using this formula, which is maximum value minus
minimum value divided by the number of classes that you have decided in the first point.
Then, starting with the minimum value, we keep on adding the glasswork to get the buckets, and once
we have the buckets, we just need to assign the number of observations belonging to each bucket.
So let's do it and an example for better clarity.
Suppose we have the following numbers as customer ages.
We want to group this data first, we will select the number of groups we want to create.
So let's say we want to create five buckets.
Next, we find out Glassford using the formula.
So 34 minus seven, the highest value minus the lowest value divided by the number of classes that we
decided, which is five, which comes out to five point for which we are down to five.
Now, starting with the lowest value we are declasse, worked to get 12, so first classes seven to
12, next is 13.
We again at the Glassford and we get 18.
So 13 to 18 is the next class.
And we continue to do so.
We get the last Latvijas 31 to 36.
The next column is called Tele.
We put a mark for each value that belongs to that category, so the first value N belongs to seven to
12 category.
So we put a marker, the next value 14 belongs to 13 to 18 category.
So we put a line here and we continue to do so till we get to the last value, which is 33, which belongs
to the 31 to 36 category.
You can also notice that the airport is landing without Lane having this land line, Heilprin counting
the last column is the only count of these lanes.
So first category has two lanes, seconders four and the last one with this large lane, which means
five and three more as it frequency.
We have this table, which has the frequency distribution.
When we plot the frequency distribution of quantitative data, it is called Instagram.
I have created this in PowerPoint only it is a little bit different than the table we created because
the limits are in decimal point, so it is starting from seven to twelve point four.
And from twelve point four to seventeen point eight, because the actual value of the glass was it was
five point four.
We don't add it to five for our convenience.
Like Bajaj, Instagram is also representing the frequency values of each class.
So whenever you get a data, it is good to plot a histogram so that you get the distribution of your
data.
So as you can see from this graph.
Most of the customers belong to the category of 28 to 34.
And very few customers belong to age less than 23.
So we have very few teenagers, but we have a lot of young customers.
Next, we look at some common shapes of histograms.
There are three properties here.
One is Cemetery City, second is Skewness, and third is uniformity.
Asymmetric variable distribution is seem about decentered.
You can see that left is the mirror image of the right.
So these two types, asymmetric.
If higher frequencies are more shifted towards one side and the other side has lower frequencies, then
the graph is skewed as represented in these two graphs.
If the frequencies are uniformly distributed in all the classes, then the graph is uniform.
If you go back to the histogram withdrew earlier, you can see that it is a skewed data.
The frequency of the last class is higher and frequency of the previous classes is much lower.
It does not have some atrocity sense, if you look at left part of this graph, it does not seem as
part of this graph and it is not uniform, since all the different classes have very different values.
In the end, we will look at an important probability distribution called the normal distribution.
It occurs very often in the recorded data, and very often we make assumptions that the data is normally
distributed.
What this means is that our data is a continuous numerical data, and the probability density at that
point is actually a function of the distance of that point from the mean of that data.
It is represented by this formula.
We don't need to remember this formula, just notice that the height by which is diplomat didn't get
any point is a function of the distance of that particular value from the mean.
So X minus new distance from the main determines the probability density at any particular point.
So when we have such data and we draw a histogram of such data.
So if we create a number of classes and we assign the value, the frequency, distribution of values
in that classes, it will be drawn something like this to the shape will resemble this.
So in simple terms, what this graph is representing is the value at mean as maximum probability of
occurrence.
And as you go farther from the mean on either side, the probability of occurrence decreases.
Also note that since Y denotes probability, identity and not probability, therefore, to get the probability
of occurrence between a range, you will have to calculate the area under the graph.
So, for example, if you want to find out the probability of occurrence of.
Value, which is less than they mean it will be area on the left of the side of the graph and this will
be half of the total area.
We'll discuss how to calculate this area and how to calculate this probability, these software packages
which we are using in this course, will automatically give us the probability for any change that we
want to calculate.
Listed, there are three properties of normal distribution.
The total area under the covers, one because this graph is showing the probability identity.
So if you want to find the probability of all values happening, it is one.
The curve is symmetric.
And these two tables at the end, these extend indefinitely.
We won't go deeper than this for normal distribution.
And that is all we need for what we are going to learn later in the course.
That's all for this.
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