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 table. It 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.
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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:
Score (X) | Frequency (f) |
Below 75 | 4 |
76 - 80 | 14 |
81 - 85 |
2 |
86 - 90 |
8 |
91 - 95 | 5 |
96 - 100 |
1 |
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.Scores (X) | Tally Mark |
118 - 125 | lll |
126 - 133 |
llll |
134 - 141 |
lll |
142 - 149 |
ll |
Scores (X) | Tally Mark |
Frequency (f) |
118 - 125 | lll | 3 |
126 - 133 |
llll | 4 |
134 - 141 |
lll | 3 |
142 - 149 |
ll | 2 |
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.
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.
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?
Below you could see some examples>:
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.
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 |
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.
(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%
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Frequency Distribution | Cumulative Frequency |
Relative Frequency Table Example | |
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