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Frequency distribution table is a representation of the frequencies related to the various possible outcomes in a sample. Each of the entries in such a table comprises the frequency or count pertaining to the occurrences of the values concerned in the respective interval or group.
- Both qualitative and quantitative variables can represent the frequency distribution table.
- It uses the concept of statistics to determine how specific values occur in the dataset.
- A frequency distribution table collects, documents, and stores information about our daily lives.
- Within the table, data is divided into intervals.
- It summarises the information under categories and their frequencies.
- The qualitative variables in a frequency distribution table may include brands, hair colours and academic degrees.
- The quantitative variables may include odd numbers, even numbers, and bank account balances.
- Healthcare researchers can use frequency distribution tables to test the effect of new medicines.
Key Terms: Frequency distribution table, Statistics, Grouped Data, Variable, Ungropued Data, Bar Graph, Pie Chart, Histogram, Frequency, Cumulative Frequency Distribution, Variance, Types of Frequency Distribution Table
Types of Frequency Distribution Table
There are various types of frequency distribution table in terms of frequency as far as presentation in a tabular form is concerned which are as follows:
Grouped Frequency Distribution Table
Grouped Frequency Distribution facilitate the ease of the derivation of insights from observations, grouping into class intervals is sometimes the key thing. It involves the following:
- Calculation of the minimum value and the maximum value of the data set in question
- Division of such a range through the number of groups intended to be prevalent in the analysis
- Segregation of the data within the respective sub-group taking account of the width of the class concerned
- Calculation of the frequency of the data prevalent within the respective group
Ungrouped Frequency Distribution Table
The ordering of the values in an Ungrouped Frequency Distribution is from minimum to maximum. It involves the following:
- Listing of the values bearing uniqueness in the first column
- Calculation of the repeated instances of each and every value bearing uniqueness and recording it.
Cumulative Frequency Distribution Table
The Cumulative Frequency Distribution is a result of the addition or subtraction of all the previous class intervals for the purpose of determining a specific class interval in terms of presentation in a tabular form.
It involves the following:
- Calculation of frequencies for every category
- Arrangement in ascending or descending order in accordance with the categories or class intervals.
- Adding all the preceding frequencies.
Additionally, in this kind of distribution, the class intervals do not bear a range but represent a conclusion which is logical in nature such as being either greater than a threshold value or less than a threshold value.
Example of Cumulative Frequency DistributionExample: The frequency of the second category is calculated when the individual frequencies of the first and second categories are added. |
Read More:
| Chapter Related Concept | ||
|---|---|---|
| Empirical Probability | Venn Diagram | Rolle’s Theorem |
Relative Frequency Distribution Table
The presentation of Relative Frequency Distribution in a tabular form displayed the daily usage of statistical applications, referring to the proportion pertaining to observations related with each category.
- The calculation is done when individual class intervals are divided by the total number of frequencies observed.
- The writing of the relative frequencies can be done through percentage, decimal points and fraction.
- When all the preceding relative frequencies are added, it results in cumulative relative frequency.
Example of Frequency Distribution TableExample 1: The marks obtained by 10 students out of 20 in an examination are presented in a tabular form as:
The frequency implies the occurrence of data the number of times in a data set. Observing the table, it is understood that the frequency is the number of students who obtained the marks. Such a table indicates a Grouped Frequency Distribution.
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Example 2: The weight of 100 people in a locality in presented in a tabular form as:
As observed from the first column of the table, the class interval is represented through a class width of 10. In each of the classes, the lowest number indicates the lower limit of the class and the highest number indicates the upper limit of the class. For example, in the class of 50-59, the lower limit of the class is 50 and the upper limit of the class is 59. | |||||||||||||||||||||||||||||||||
Data Collection in a Frequency Distribution Table
In a Frequency Distribution Table, the collection of data implies the concept of statistics which also includes analysis, observation and presentation. Statistics facilitates predictions related to the nature of data on the basis of the relevant data previously available.
- Statistical data collected can be represented through tables, frequency polygons, bar graphs, histograms and pie charts.
- Collection of data in an effective and efficient manner is very important.
- It involves the processing of vital information as far as recording.
- It subsequently maintain records for concerned data.
- Such data should also be organised in the manner as desired as far as the frequency distribution table is concerned.
Representation of Statistical Data
How to construct a frequency distribution table?
The steps to create a frequency distribution table are as follows:
- First, create a table with two columns and as many rows as possible depending on the type of variable.
- Determine whether you need to draw an ungrouped or grouped frequency distribution table.
- Write the value of data in the first column of the frequency distribution table.
- Count the number of times a value is appearing in the data set.
- Note down the frequency of the variable in the second column of the table.
- Add the total number of observations in the last row of the table.
Uses of Frequency Distribution Table
Various uses of frequency distribution table are as follows:
- A company's annual profit report can be prepared using the frequency distribution table.
- It is used in forecasting the weather conditions of an area based on various parameters.
- The table can be used to analyse the performance of students in school.
- It can be used in politics to study how the public feels about the elected candidate.
- The sales team can use a frequency distribution table to get insight into customer behaviour and identify areas of improvement.
Advantages of Frequency Distribution Table
Various advantages of the frequency distribution table are as follows:
- The frequency distribution table provides an organized presentation of data.
- It helps you identify patterns easily.
- The table provides simpler interpretations of the data set.
- It helps in the calculation of central tendency and variance.
Things to Remember
- The frequency distribution table is used to determine the number of observations for each set of variables.
- Grouping and ungrouping aspects need to be identified for the creation of the table.
- Next, determine the range to be taken into consideration for each data set.
- The frequency distribution table helps in organizing the data to be found.
- It helps in making a chart, which in turn summarizes the values and their frequencies.
Read More:
| Class 9 Mathematics Related Concepts | ||
|---|---|---|
| Mean of Grouped Data | Bayes Theorem | Measures of Dispersion |
| Mode of Grouped Data | Mode Formula | Remainder Theorem |
Sample Questions
Ques. Give an example of range in a Frequency Distribution? (1 marks)
Ans. In a cricket match, the runs scored by 11 players are as follows:
22, 3, 41, 105, 12, 35, 73, 8, 1, 6, 0
The range is 105 the difference between the highest value (105) lowest value (0) is 105
Ques. Present a table of Joint Frequency Distribution? (2 marks)
Ans. The table is as follows:
| Category | Cooking | Baking | Total |
|---|---|---|---|
| Men | 5 | 10 | 15 |
| Women | 12 | 3 | 15 |
| Total | 17 | 13 | 30 |
In the two-way contingency table, the total row and total column present marginal distribution and the body of the table presents the joint frequency.
Ques. Represent data regarding the pocket allowances of students through a Frequency Distribution Table? (2 marks)
Ans. The table is as follows:
| Monthly Pocket Allowances (in Rs.) | Number of Students |
|---|---|
| 1000-1400 | 5 |
| 1500-1800 | 4 |
| 2000-2500 | 1 |
| Total | 10 |
Ques. Represent data regarding the height of people in a locality through a Frequency Distribution Table? (3 marks)
Ans. The table is as follows:
| Height (in cm.) | Number of People |
|---|---|
| 145-150 | 8 |
| 150-160 | 10 |
| 160-170 | 16 |
| 170-180 | 4 |
| 180-185 | 2 |
| Total | 40 |
Ques. Represent data of goals scored by players of a team in a football tournament through a Frequency Distribution Table? (2 marks)
Ans. The scores in the recent games is 1,2,1,3,2,3,1,2,2,2
| Score | Frequency |
|---|---|
| 1 | 3 |
| 2 | 5 |
| 3 | 2 |
Ques. Represent data of magazines sold in a shop in the last 3 days through a Frequency Distribution Table? (2 marks)
Ans. The numbers are : 30, 11, 17
| Magazines sold | Frequency |
|---|---|
| 30 | 1 |
| 11 | 1 |
| 17 | 1 |
Ques. Represent data of the values recorded when number cards bearing numbers 1 to 4 are flipped 5 times through a Frequency Distribution Table? (2 marks)
Ans. The values are : 4,3,3,1,2
| Values | Frequency |
|---|---|
| 1 | 1 |
| 2 | 1 |
| 3 | 2 |
| 4 | 1 |
| Total | 5 |
Ques. Represent data of the blood groups of students participating in a school blood donation camp through a Frequency Distribution Table? (3 marks)
Ans. The blood groups of 12 students were reported as follows:
A, B, AB, A, AB, AB, A, AB, AB, AB,O,B
| Blood Group | Number of students |
|---|---|
| A | 3 |
| B | 2 |
| O | 1 |
| AB | 6 |
| Total | 12 |
Ques. Represent data of the vegetarian and non-vegetarian food items available in a restaurant through a Frequency Distribution Table? (1 mark)
Ans. The table is as follows:
| Type of Food | Frequency in menu |
|---|---|
| Veg | 10 |
| Non-veg | 6 |
| Total | 16 |
Ques. The weekly pocket expenses (in dollars) of a group of 25 students chosen at random are shown below.
37, 41, 39, 33, 41, 27, 45, 31, 48, 32, 44, 39, 35, 39, 30, 49, 27, 36, 33, 38, 49, 45, 40, 39, 35
Make a grouped frequency distribution table with class intervals of equal width beginning with 25 - 30, 30 - 35, and so on. Determine your weekly out-of-pocket expenses as well? (3 Marks)
Ans. The following data is represented in the table:
| Weekly Expenses | Number of Students |
|---|---|
| 25-30 | 2 |
| 30-35 | 6 |
| 35-40 | 8 |
| 40-45 | 5 |
| 45-50 | 4 |
| Total | 25 |
The smallest value in the given data is 27 and the largest value is 49. So, the weekly pocket expense range = 49 - 27= $22.
Ques: Sana and Asha have a deck of one-to-ten number cards. They take out a number card and record the number that appears on it. They go through the process at least 12 times. They have the following values assigned to them:
5, 8, 9, 2, 3, 7, 3, 1, 6, 9, 3, 7
Create a frequency table to better organise the data? (3 Marks)
Ans: The following data is represented in the table:
| Values | Frequency |
|---|---|
| 1 | 1 |
| 2 | 1 |
| 3 | 3 |
| 4 | 0 |
| 5 | 1 |
| 6 | 1 |
| 7 | 2 |
| 8 | 1 |
| 9 | 2 |
| 10 | 0 |
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