Frequency Distribution

What is the Frequency Distribution in Statistics?

Frequency distribution, a function in statistics, is used to reflect the different results of a particular frequency in the form of a table, and/or graph depicting how many times a specific value has appeared in a group or an interval.

To calculate the frequency in the excel, we need to apply the Frequency Distribution formula in the cell where we want the result to be reflected.

 =Frequency(data_array, bins_array)
  • Data: To express information, whether numerical or non-numerical, if collected together, is known as data. For instance, the names of students and marks scored by them.
  • Data Array: It is the group of numerical or non-numerical information required for frequency distribution. Generally, it is a group of data available for consideration.
  • Bins Array: It is the interval created to group the data for required frequencies. For instance, if we want to make multiple frequencies for marks scored by students, it could be 0-09, 10-20, 21-30, and so on.

Explanation

As per the frequency distribution formula, we get an idea of the count of a particular frequency (group or a number) in the raw data set. As the group of data doesn’t provide any fruitful information, the frequency distribution adds value to it by segregating the data into given frequencies or groups. From observing the above table, it is visible that there is only one household that does not have any parking available. Other than that, almost all the houses have at least three parking spaces available.

Frequency-Distribution-Formula

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Examples of Frequency Distribution

You can download this Frequency Distribution Formula Excel Template here – Frequency Distribution Formula Excel Template

Example #1

Let’s take an example to deepen the understanding of the frequency Distribution Formula. In a local neighborhood of the Santa Clara, California, each home has multiple car parking facilities. The following are the number of slots available in each house for car parking.

Example 1 (given Data)

Solution:

Steps to create Frequency Distribution in Statistics:

  • First of all, we will calculate the number of intervals. The intervals here is one car, two cars, three cars, and so on.
  • Now, we will create a table with two columns; the number of car parking figures and the frequency of those intervals. The heading of the column would be Car Parking Available, and Frequency.
  • Now, we will use the frequency formula of excel by entering = sign in the cell where we need results, i.e., cells of the Frequency column. We will put =frequency and enter tab ( it will automatically select the frequency formula from the drop-down list) and select the raw data as data array(A4:A23). Then we will put a comma (,), then we will move ahead to select the entire data of intervals (C4:C9) created by us in the bins array part. Now, we will put the closing bracket( parenthesis) or simply hit enter. The formula is complete, and we will see the result displayed in the cell.

The formula would look like this.

=FREQUENCY(A4:A23,C4: C9)
Frequency Distribution Formula Example 1-1
  • But, the result displayed is not accurate as in the statistical formulas where the array is used in the calculation, the result tends to deviate from being exact. So, we will use the Curly Braces { } to resolve this issue. The curly-brace helps the formula to fetch exact results.
{=FREQUENCY(A4:A23,C4:C9)}
  • We will go to the first cell where we have put the formula initially, and press F2 followed by Ctrl+Shift+Enter. Now the resultant answer is complete.
Frequency Distribution Formula Example 1-3

Example #2

Let’s calculate the frequency of the marks obtained by students in the Science subject.

The table of the marks obtained by students is as follows: 

Example 2 (Given Data)

Solution:

To calculate group frequency distribution, we need to follow the below-mentioned steps:

  • First of all, we need to create three columns; From, To, and Frequency. Here, in From and To, we will take the highest to the lowest number based on the data set. We took the lowest number as zero and the highest as 99 for calculation of frequency distribution.
  • Secondly, we will take the highest numbers as intervals in the next column.
  • We will put the frequency formula Frequency(data_array, bins_array). Here the data array is from B4: B23, and the bins array is F4: F13. This formula is put in the cell where we need the result, and select data array and bins array by selecting marks obtained and intervals.
Frequency Distribution Formula Example 2-2
  • Now we will apply the curly braces by using F2, Ctrl+Shift+Enter. Now we have the required results. After putting the entire formula, it will look like this:
{=FREQUENCY(B4:B23,F4:F13)}
Frequency Distribution Formula Example 2-3

So, the frequency distribution provides a more informative approach to the raw data. Here it shows the frequency of different marks scored by various students in the class. For example, 11 students have got marks between 50 – 70.

Example #3

Let’s calculate the frequency of the cars manufactured by various brands across the globe.

Example 3 (Given data)

Solution:

  • First of all, we will put the highest and lowest data in the From and To columns derived from the Cars manufactured column in the example.
  • Then we will assign the numbers in the frequency table in descending order. Now, we will apply the frequency formula mentioned above in the curly brackets. We will put the frequency formula Frequency(data_array, bins_array).
  • Here the data array is from B4: B15, and the bins array is F4: F12. This formula is put in the cell where we need the result, and select data array and bins array by selecting marks obtained and intervals. Now we will apply the curly braces by using F2, Ctrl+Shift+Enter. Now we have the required results.

After putting the entire formula, it will look like this:

{=FREQUENCY(B4:B15,F4:F12)}
Frequency Distribution Formula Example 3-1
  • We have received the results of various frequencies in the Frequency column showing the number of companies involved in manufacturing cars for that particular category.
Frequency Distribution Formula Example 3-2

After observing the above table, we could make a rough estimate of the range of production of cars by various brands. Such as the table shows that the product range of 10 – 19 has been met by three car manufacturers.

Relevance and Uses

  • It is a method to understand the information contained in the raw data provided. It explains how many times a particular number or observation comes in the set of one data.
  • It helps us to find a pattern in the given data set. For example, if we take the first example, we could easily conclude that almost all households have a car parking facility as there is only one house where there is no parking arrangement.

This article has been a guide to Frequency Distribution in Statistics and its definition. Here we discuss how to calculate frequency distribution along with practical examples and a downloadable excel template. You can learn more about statistics and excel modeling from the following articles –

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