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# Frequency Histogram

Top
 Sub Topics In the statics, the information can be represented by the help of a frequency histogram. In the histogram graph the rectangles are used to show the frequency of data items in form of successive intervals. The independent variables of a given data items are plotted along the horizontal axis and the dependent variables of a given data item are plotted along the vertical axis. We need to follow some steps for designing the histogram: Step1: First we select the data for making the histogram. Step2: After that we plot a graph, and we know that along the horizontal axis the independent variables are plotted and the dependent variables are plotted along the vertical axis. Suppose we have the data values, 2 items in between 5 to 6, and 1 items are in between 6-7 and 6 item is in between 7 to 8, 4 items are in between 8 to 9, 5 item in between 9 to 10, 2 item in between 9 to 10 and 3 item in between 10 to 11. For making a histogram graph we have to follow all the above steps: Step1: First we select the data item i.e. We have the data values, we have 2 items in between 5 to 6, and 1 item are in between 6-7 and 6 item is in between 7 to 8, 4 items are in between 8 to 9, 5 item in between 9 to 10, 2 item in between 9 to 10 and 3 item in between 10 to 11. Step2: For this histogram the value of variable represents the horizontal axis and the frequency of the variable represents the vertical axis. This is how we plot a frequency Histograms.

## Relative Frequency histograms

The Ratio of the value to the total number of the given values is known as the Relative Frequency Histogram.
For example: If we have to select 15 trains from 50 trains then the relative frequency of a histogram is:
Then the frequency of trains is 15, and the relative frequency of trains is 15/50 because we know that it is the ratio of actual number to the total number of values.
Now we will see how to find relative frequency Histograms.
For finding the relative frequency of a histogram we have to follow some steps which are:
Step 1: First we have a number.
Step 2: Now find the frequency.
Step 3: If we have the value of frequency, then with the help of frequency we can find the relative frequency of a histogram.
Suppose we are looking for the brands of the car and we have 18 observations:
Suzuki, Audi, Mercedes, Audi, Honda, Mercedes, Audi, Hyundai, Mercedes, Honda, Suzuki, Hyundai, Mercedes, Audi, Honda, Suzuki, Audi, Mercedes
Here we have to find the relative frequency of the given combinations?
For finding the relative frequency of an object we have to follow all the above steps:
Step1: First find the number.
Step2: Now we have to find the frequency of all the brands Combination of a car.
So the frequency of Suzuki car is: 3;
The frequency of Audi car is: 5;
The frequency of Mercedes car is: 5;
The frequency of Honda car is: 3;
The frequency of Hyundai car is: 2;
By using the definition of the relative frequency we can easily find the relative frequency:
So the relative frequency of Suzuki car is 3/18;
The relative frequency of Audi car is 5/18;
The relative frequency of Mercedes car is 5/18;
The relative frequency of Honda car is 3/18;
The relative frequency of Hyundai car is 2/18.
For example: If you select 20 colleges from the 150 college:
Then the relative frequency of a college:
Solution: The frequency of a college is 20;
And the relative frequency of college is 20/150.

## Frequency Distribution Table

There is a statistical approach to simplify a large sample of data values by constructing a Frequency distribution table. It is a simple method of shaping and simplifying the data values to make their statistical analysis more understandable.
Main objective of making a frequency distribution table is to analyze how frequently each value occurs within a particular Set. Number of occurrences of any value is termed as its frequency in distribution table. So, we draw a table consisting of two columns, with first column representing all possible set of data values and second column shows their respective frequency of occurrence.
Let’s consider an example to understand it. Say we have a data set that consists of following 25 Numbers: 1, 3, 5, 0, 7, 5, 8, 9, 2, 6, 6, 13, 20, 24, 34, 43, 12, 23, 5, 10, 5, 2, 5, 6 and 8.
We first have to reorganize the data values in a particular order, let say we rearrange them in descending order to simplify our calculations: 0, 1, 2, 2, 3, 5, 5, 5, 5, 5, 6, 6, 6, 7, 8, 8, 9, 10, 12, 13, 20, 23, 24, 34 and 43. Once the reorganization of data is complete, make two columns: one for data values and the other for frequency of occurrence.
Analyzing first value in arrangement i.e. 0; we see that it has frequency of occurrence as 1 in complete set. In similar way we can evaluate the frequencies for other data values also. Frequency Distribution Chart can now be drawn as follows:

DATA VALUE

FREQUENCY OF OCCURRENCE

0

1

1

1

2

2

3

1

5

5

6

3

7

1

8

2

9

1

10

1

12

1

13

1

20

1

23

1

24

1

34

1

43