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Frequency Table

An important branch of mathematics that deals with gathering, organizing, estimating and interpreting the vast numerical data for a survey or a research, is known as statistics. There may be one or more numbers of statistical data that are used more than once. The number of times a particular data item is utilized, is known as its frequency.

When the distribution of frequencies is listed in a table OR 
tabular presentation of frequency distribution, known as frequency tableIt is used to list out one or more variables taken in a sample. Each sample contains an individual frequency and each frequency is distributed with an interval between each frequency. It is also of two types that is univariate and joint. Frequency distribution can be defined as a summary presentation of the number of observations of an attribute or values of a variable arranged according to their magnitudes either individually in the case of discrete series or in a range or class interval in the case of both discrete and continuing series.

Classification of data can be done in several ways but only quantitative classification gives rise to the formation of the frequency distribution.

Related Calculators
Frequency Calculator Calculate Relative Frequency
Frequency and Wavelength Calculator Frequency Distribution Calculator
 

Frequency Distribution Table is a way to organize data. A frequency distribution table is an organized tabulation of the number of individual events located in each category. It contains at least two columns, one for the score categories (X) and another for the frequencies (f). Below we have explained briefly for you to understand the concept of frequency table better and workout frequency table example:

Solved Example

Question: Here is the list of marks obtained for the students in the examination. Find the number of students who got more than 85 marks, More than 95, Less than 80 more than 76.

 Score (X)   Frequency (f)
 Below 75        4
 76 - 80       14
 81 - 85
       2
 86 - 90
       8
 91 - 95        5
 96 - 100
       1

Solution:
 

From the table we can conclude that:

Students who got more than 85 = 8 + 5 + 1 = 14

Students who got more than 95 = 1

Students who got less than 80 more than 76 = 14.
 

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How to Make?

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Steps to design:

Step 1:
Collect a specific set of data to plug into the table.

Step 2: Arrange the data into different groups called classes with their corresponding frequencies.

Step 3:
The 1st column shows what is being arranged in ascending order and another for the frequencies.

Step 4:
Tally the data into classes. Each data value falls into exactly one class. Count the tally's and record result.


Two types: Cumulative and grouped tables

The cumulative frequency is a total of frequencies through the classes of a frequency distribution. The cumulative frequency for each class interval is the frequency for that class interval added to the preceding cumulative total. Cumulative frequency can also be defined as the sum of all previous frequencies up to the current point. The cumulative frequency is useful when representing data using diagrams like histograms.


Grouped frequency distribution tables are used to organize and simplify a large set of data into smaller groups. The values are grouped in intervals that have the same amplitude. Each class is assigned its corresponding frequency. The group frequency distribution is essentially a table with two columns. The first column represents all possible 'grouping' of the data and the second column represents 'frequency'. 

Frequency Table with Intervals


Grouped Frequency Table

Here, the frequency tells us how many times a particular data appears. For example, 11-15 marks have been scored by two students. The data so distributed is called frequency distribution and the tabular form is called frequency distribution table.

Solved Example

Question: Count the number of items in each class, and put the total in the second column. Total scores of the students obtained in examination are: 118, 124, 125, 127, 128, 130, 133, 136, 137, 140, 142, 149.

Solution:
 
Given data: 118, 124, 125, 127, 128, 130, 133, 136, 137, 140, 142, 149.

Frequency Distribution Table:

Step 1:

Arrange the data into different classes with their corresponding frequencies mark as telly symbols.

 Scores (X)  Tally Mark
 118 - 125  lll
 126 - 133
 llll 
 134 - 141
 lll
 142 - 149
 ll

Step 2:
Count the tally marks and record the frequencies (result).

 Scores (X)  Tally Mark
Frequency (f)
 118 - 125  lll  3
 126 - 133
 llll   4
 134 - 141
 lll  3
 142 - 149
 ll  2


 


Frequency Table of Categorical Data

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In statistics, categorical data involves a variable that classifies the subject into one of a number of categories. Since the data will generate descriptions as opposed to numbers, means and deviation do not apply. In these cases, data is exploring using the frequency tables and bar charts. In order to create tables for categorical data, count the number of individuals in each class then list that in one column with the corresponding frequency in 2nd column.

Relative Frequency Table

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A relative frequency table presents the total count for each category and the relative frequency in which each category occurs. Relative frequency is the proportion of the total frequency that is in any given class interval in the frequency distribution. For a data set consisting of n values. If f is the frequency of a particular value then the ratio '$\frac{f}{n}$' is called its relative frequency.

Relative Frequency Distribution Table

If the frequency of the frequency distribution table is changed into relative frequency then frequency distribution table is called a relative frequency distribution table.

Two Way Frequency Table

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Two-way frequency tables are used to examine the relationship between two categorical variables. Bivariate categorical data of this sort can easily summarized by constructing table. Two-way frequency tables are often characterized by the number of rows and columns in the table.

Solved Example

Question:

Joint frequency table:

Marks

Student

Math

Science

English

Total

    A

80

35

29

144

    B

65

14

27

106

   C

79

32

10

121

   D

87

53

23

163


Which Student with highest total?


Solution:
 
Table contains 4 rows and 4 columns. To the right, the two-way table shows the total marks of the students. Because entries in the table are frequency counts, the table is a frequency table. From the table we can conclude that student D with the highest total.
 

Examples

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Below you could see some examples>:

Solved Examples

Question 1:

The following are the marks obtained by 50 students in a mathematics test. Prepare a frequency table for the data.

45, 68, 41, 87, 61, 44, 67, 30, 54, 8, 39, 60, 37, 50, 19, 86, 42, 29, 32, 61, 25, 77, 62, 98, 47, 36, 15, 40, 9, 25, 34, 50, 61, 75, 51, 96, 20, 13, 18, 35, 43, 88, 25, 95, 68, 81, 29, 41, 45, 87.


Solution:
 

Step 1:

To decide the length of the class interval and to take all the scores given in the problem, we have to look in the largest value and the smallest value from the given scores. We can do this by merely going through all the scores. Here, the largest value is 98 and the smallest value is 8.

The difference = Largest value - Smallest value.

= 98 - 8

= 90.

Step 2:

For the above problem we form a frequency table taking class intervals 0 - 10 , I0 - 20 , 20 - 30 , 30 - 40, 40 - 50, 50 - 60, 60 - 70, 70 - 80, 80 - 90 and 90 - 100.


Step 3:

The first score is 45. It lies in the class interval 40-50. Therefore put one tally mark ( vertical bar like ' l ') in the class interval 40 - 50. The next score in the first row is 68 one by one, identify the class intervals in which they lie and put a tally mark in the corresponding class interval.


Step 4:
The tally marks in each class interval are counted and the counted number is put against the same class interval under the frequency column. All the frequencies are added and the number is written as the total frequency for the entire class intervals.

Class Intervals

Tally marks

Frequency

0-10

ll

2

10-20

llll

4

20-30

llll l

6

30-40

llll ll

7

40-50

llll llll

9

50-60

llll

4

60-70

llll lll

8

70-80

ll

2

80-90

llll

5

90-100

lll

3


Total

50


 

Question 2:

Using frequency table, determine the key: F = Football, C = Chess, B = Badminton, every letter below indicates a student joining the sports association.

F C B F B F C B C F
B F C B C F B C F C F


(a) Create a frequency table for the information

(b) Try to calculate which club has the maximum frequency and which club has the minimum frequency.

(c) Estimate the percentage of students who joined the Badminton.


Solution:
 

(a) Initial, we should write tally club wise. We arrange the information in the frequency table

Club

Tally

Frequency

Football

Chess

Badminton

|||| |||

|||| ||

|||| |

8

7

6


(b) Observing the frequency table, we should calculate maximum and minimum frequency of club. Football is the club with the maximum frequency and tennis is the association with the minimum frequency.

(c) Total Percentage of students who joined to the football association.

= `8/21` *100%

= 30%


 

More topics in Frequency Table
Frequency Distribution Cumulative Frequency
Relative Frequency Table Example
NCERT Solutions
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