Measures of Frequency

(Intro: 16 sec)

In this chapter, we will see the, first type, which is measures of

frequency.

So, let's continue.

First, we will see what frequency is.

Frequency is the number of times a value of the data occurs.

This means that, suppose I have a particular data, in that particular data, how many times my value has repeated.

Let’s take an example, I have 20 kids in a particular class.

I asked them, “how many hours per day do you work?''

How many hours do they work per day? So, the responses that they gave were in hours.

and those responses were of these kinds, 5 hours, 6 hours, 3 hours, 3 hours and so on.

Now what I did is, how much ever work per hour was there, I created that in a table form.

In which 2 hours, 3 hours, 4 hours, I wrote that particular time, and how many times has it been repeated in my particular data set, I counted that number and wrote it in a frequency column.

So, you will see that in this data set, 2 is repeated twice.

2 hours are at the start, and then in the middle and one is at the end.

So, the frequency is 3 times of 2.

My 3 has been repeated 5 times in the entire data set.

My 4 has been repeated thrice.

In the same way,  the number of times any number has been repeated is called its frequency.

We have arranged this table in ascending order of working hours per day.

You must be thinking this 20 that there were, 20 kids in total, that was basically my sum of frequency columns.

Because you see, how many times they are repeated, that will not be more than 20 in total because I had 20 kids so I will get the responses of 20 kids only.

That’s why, the total of this frequency column, would be my total number of students.

Coming forward, we have got a very important term which we call frequency distribution, distribution like its name suggests, whichever frequency has come to us, how we can distribute it.

That we can distribute in any form.

We can do a graphical representation; we can represent them in the form of a table.

So, let's come see about it.

So, the frequency distribution of any data is a tabular summary.

It means we arrange it in a form of a table in which we see the frequency of the particular item and whichever values are there of the frequency, those are brought in several non-overlapping classes.

Now what is the meaning of non-overlapping classes? It means that any particular category can happen only once.

It means, the value of working 2 hours, I cannot put in the value of working 3 hours.

I will have to create a different category for everyone.

This means that, frequency distribution is one graphical representation of my frequency table.

Now there are two things that have come in it, frequency table and graphical representation.

Frequency table is nothing, but it describes how many times my one particular data is getting repeated, like we saw in the previous table.

We can create our frequency distribution through some methods, like through frequency tables, through histograms, through bar charts, through pie charts.

Come let's see, what are the different ways of frequency distributions.

So, I have 4 different types of frequency distributions.

First is ungrouped frequency distribution.

Second is grouped frequency distribution.

Third is relative frequency distribution.

Fourth is cumulative frequency distribution.

Now we will come to the first type.

Ungrouped frequency distribution.

Like its name suggests, we don’t do any grouping in it.

In this we take one particular frequency of any item, of the separate data, rather than groups.

So, if I take the same example.

In this, I have put work per hour in one particular value and I created its frequency of ungrouped data.

We don’t take class intervals in this, and we find accurate frequency of individual frequency.

Second is my grouped frequency distribution.

Now you must be thinking that, I must be having hours in work per hour scenario, but suppose if someone tells you that I want to know till 4 hours, how many kids worked, how many kids worked less than that and how many kids worked more than that.

So, what you will do is, you will take this particular table, in which there are your individual frequencies.

You will draw a mark on 4.

Now you will see, what is the value less than 4, 2 and 3.

In front of 2 and 3, whatever frequency is written there, you have to sum both, and put in the less than 4 hours frequency.

Like 3 plus 5 equals to 8.

So, my less than 4 hour frequency will be 8.

Which means one class frequency is 8.

Now I have to find out, equal to four hours, people who worked equal to 4 hours.

That value is given to me which is 3 hours.

So, I have put 3 in the frequency.

Now I have to find out more than 4 hours of frequency.

More than 4 hours means they must have worked 5 hours, 6 hours and even 7 hours.

The frequencies respective to them.

6 plus 2 plus 1 equals to 9.

So, this particular table has been created.

In which, I have divided work per hour in different categories, I have divided it in different classes and created frequencies respective to them.

So, this particular data we call has grouped frequency distribution, where the frequency of every data denotes a particular class interval.

Whatever is the data, it is arranged in different groups, we call those as the class intervals.

Next is my relative frequency distribution.

What does relative frequency mean? That it must be relating to something, or the other thing.

This means that, it tells me the proportion of the total number of observations associated with each category.

Let’s say I have a particular data.

Okay.

If I divide this particular frequency data, if I divide every value, every frequency with, the total number of students.

This means that if I divide 3 by 20.

My relative frequency will be 0.15.

If I divide 5 by 20.

My relative frequency would be 0.25.

So, in this way we define our relative frequency in different terms, like, we can write it in fractions, we can write it in percentages, we can even write it in decimals.

And the total sum of our relative frequency column would be 1.

If you make a sum of 0.15, 0.25, 0.15, of all these values.

So, my final value would be 1.

So, in this way relative frequency distribution gives us proportion of the total values in every category.

Next is my cumulative frequency distribution.

What is cumulative frequency distribution? This is related to our relative frequency.

This is the sum of the first  frequency, and all the

frequencies below it.

So, in my frequency distribution table, whichever is the  first value,  first frequency.

After that, whichever is my total value.

If I continuously sum it up one after the other.

So, the values that I will get, that we call cumulative frequency distribution frequency.

For example, if we see in the same particular scenario where I have different work per hour, I have frequencies, I have relative frequencies.

Now, if I want to find the column of cumulative frequency.

What will I have to do? I have written my first value as it is, which is 0.15.

To calculate the next value, I will take the previous value and I will take the current value like 0.15 and 0.25.

I will add them both, and it will be 0.4, which is my cumulative frequency of second value.

To calculate the third value, I have taken the previous value which is 0.40, which has come now into my data and I added that with my next value which is 0.15.

So, my final value will be 0.55.

In the same way we add the total values with previous values and finally, we get a column of cumulative frequency.

In this the last cumulative frequency value that is there, that is basically the total sum of all the frequencies, which is generally always 1.

So, that we have that clarity, that whatever total sum we have done that should be 1.

Like, we had seen in relative frequency that the last value of sum is 1.

In the same way, in cumulative relative frequency as well, the last value’s sum is 1.

These are our different types of frequency distributions.

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 (outro 15 sec)