Frequency Distribution Table

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Statistics and Data: || Methods of Collecting Data:

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Outline:

Introduction

Simple Frequency Distribution

Frequency Table using PYTHON

Grouped Frequency Distribution Table

Introduction

The most common method of organizing and presenting data is table construction. Creating a frequency distribution table is the most popular approach to tabulate data. This could be accomplished by categorizing the data and recording the number of observations that fall into each category.

When the researchers have gathered all of the necessary information, the following step is to organize and present it using proper tables and graphs. This section demonstrates how to present and display facts in a clear and comprehensible manner. Students will discover how to create frequency distribution tables for both quantitative and qualitative data.

Types of Frequency Distribution Table

Simple frequency distribution, ungrouped frequency distribution, and grouped frequency distribution are types of tabular presentations.

Simple Frequency Distribution

Categorical frequency distribution is another term for simple frequency distribution. This is used to keep records that can be categorized. In other words, in this type of tabular presentation, qualitative or categorical data is appropriate.

Consider the following data give the results of a sample survey. The letters A, B, and C represent three categories. Construct a frequency distribution table from the given data below;

	A	B	A	A	C	C	A	C	C	C
	C	B	C	B	B	C	B	B	B	C
	B	C	C	A	C	C	C	B	C	A

Solutions:The categories have three letters A, B, and C, so the frequency distribution table is shown below:

Table 1. Frequency and Percent Distribution of the Categories A, B and C

Category	Frequency	Percentage
A	6	20%
B	9	30%
C	15	50%
Total	30	100%

Frequency Table using PYTHON:

Suppose the file is located in the local file directory "E:\python\TABLE1.xlsx". Then to create the frequency table using python just follow the code below:

import pandas as pd

data1=pd.read_excel('E:\python\TABLE1.xlsx',0) - Create variable name data1

table=pd.crosstab(index=data1['Category'], columns='Frequency') - create varaible name 'table' to display the table column category and frequency

table['Percent']=table['Frequency']/table['Frequency'].sum()*100 -add percent column from table

table.append(table[['Frequency','Percent']].sum().rename('Total'))-add column grand total

The output is shown below:

Grouped Frequency Distribution Table

The grouped frequency distribution table is used to exhibit data sets by classifying them and displaying the frequency of occurrences within each class.

Terminology

Let us familiarize ourselves with all of the features of the grouped frequency distribution table before we construct it.

Class Intervals

This refers to the grouping defined by lower class limit and upper class limit. Sometimes, the class limits is not defined.

Class boundaries

Class boundaries are used to divide the classes so that the frequency distribution table does not have any gaps. Continuous data, such as test scores, weights, and heights, is intended to start and stop with an accuracy of at least 0.5 class boundaries.

Class Marks or class midpoint

This is the value of a class interval or classes. This is obtained by finding the average of the lower class limit and upper class limit.

Class size or class width

Class size or class width is the difference between the upper class limit/boundary and lower class limit/boundary. The ratio of two values that is, the range divided by desired number of classes.

Class frequency

This refers to the number of observations belonging to a class interval.

Steps in Constructing the Grouped frequency Distribution

1. Determine the range (R) of the distribution. R = Highest value - Lowest value.

2. Decide the number of classes. According to Herbert Sturges, suggested that the number of classes to tabulate n items should be approximately 1 + 3.3 log (n). The class intervals, normally is not less than 5 and not more than 20.

3. Determine the class size (i). This is obtained by dividing the range by the desired number of class interval. The class width should be an odd number as possible. This ensures that the midpoint of each class has the same place value as the data.

4. Select a starting point, either the lowest score or the lower class limit. Add the class width to the starting point to get the second lower class limit. Then enter the upper class limit.

5. Find the class boundaries by subtracting 0.5 from each lower class limit and adding 0.5 to the upper class limit.

6. Represent each score by a tally that fall within the class interval.

7. Count the number of frequency for each class. Finally, get sum to determine the total frequency.

Example:

When 40 people were surveyed in a certain City X, they reported the distance they drove to the mall, and the results (kilometers) are given below. Construct a grouped frequency distribution table.

	2	8	1	5	9	5	14	10	31	20
	15	4	10	6	5	5	1	8	12	10
	25	40	31	24	20	3	9	15	20	15
	25	8	1	1	16	23	18	25	21	12

Solutions:Following the Steps:

1. Range = highest score – lowest score = 40 – 1 = 39

2. Class intervals = 1 + 3.3 log (40) ≈ 6.28 rounded of 6.

Class width = R/classes = 39/6 = 6.5 = 7 class size

4. Determine the lower class limit. In this example the lowest value is 1. So, 1 could be the lower class limit and add the class width to the lower class limit to get the next lower limit (8).

5. Determine the class boundaries. This will be obtained by adding 0.5 for each upper class limit and subtract 0.5 for each lower class limit.

6. Determine the class midpoint for each class interval.

7. Count the number of frequency for each class

Table 2. Frequency Distribution of the Distance Travelled by the Subjects

Distance(Class Interval)	Tally	Frequency	Class Boundaries	Midpoint	Less than Cumulative Frequency
1 - 7	/////-/////-//	12	0.5 - 7.5	4	12
8 - 14	/////-/////-/	11	7.5 - 14.5	11	23
15 - 21	/////-////	9	14.5 - 21.5	18	32
22 - 28	/////	5	21.5 - 28.5	25	37
29 - 35	//	2	28.5 - 35.5	32	39
36 - 42	/	1	35.5 - 42.5	39	40
Total(N)		40

(Source: Unknown)

To conclude, tables should present data in a logical, consistent way that allows the reader to comprehend and interpret the information it contains quickly and accurately. The table must include the following components: table number, title, column headings, row headers, and body. In addition, the table may have footnotes, which should be placed below the table's bottom rule.

Relevant Topics must watch here!:How to Create Frequency Distribution using Python

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I'm sure I don't have all of the information about the Frequency Distribution Table right here." I'm hoping and would love to hear your thoughts on this topic in the comment section below."

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