|
|
BOYS
|
GIRLS
|
TOTAL
|
|
YES
|
28
|
18
|
46
|
|
NO
|
22
|
12
|
34
|
|
TOTAL
|
50
|
30
|
80
|
Solution:
Calculate the marginal relative frequency for the data:
Marginal relative frequency of boys who attended the concert
= (28/80)×100 = 0.35×100 = 35%
Marginal relative frequency of boys who did not attend the concert
= (22/80)×100 = 0.275×100 = 27.5%
Marginal relative frequency of girls who attended the concert
= (18/80)×100 = 0.225×100 = 22.5%
Marginal relative frequency of girls who did not attend the concert
= (12/80)×100 = 0.15×100 = 15%
Marginal relative frequency of students who attended the concert
= (46/80)×100 = 0.575×100 = 57.5%
Marginal relative frequency of students who did not attend the
= (34/80)×100 = 0.425×100 = 42.5$
- Frequency: This refers to the count of observations in a given category.
- Marginal Frequency: This is the sum of frequencies in a row or column of a contingency table. Essentially, it is the total count of observations for a single category (ignoring other variables).
- Relative Frequency: This is the proportion of observations in a particular category compared to the total number of observations.
The relative marginal frequency formula is:
Relative Marginal Frequency = (Frequency of a Particular Category)/(Total Frequency of All Categories)
Advantages of Relative Marginal Frequency
Vrious advantages of Relative Marginial Frequency includes:
- Graphical Representation: Relative marginal frequencies are often visualized using bar charts, pie charts, and other graphical tools, making it easier to communicate findings to a non-technical audience.
- Standardization: Relative marginal frequency standardizes the data by converting absolute frequencies into proportions or percentages. This makes it easier to compare categories with different total frequencies.
- Ease of Interpretation: By expressing frequencies as proportions or percentages, relative marginal frequency provides a clearer understanding of how each category contributes to the total. For example, if 30% of respondents prefer option A, it’s easier to grasp than an absolute number of respondents.
- Facilitates Statistical Analysis: It aids in statistical analysis by providing a basis for further calculations, such as calculating relative risks or odds ratios in categorical data analysis, etc.
Two-Way Frequencies
Two-way frequencies refer to the counts of observations across two categorical variables in a data set. These frequencies are typically organized into a two-way table, also known as a contingency table, which displays the distribution of one variable across the levels of another variable. This helps in understanding the relationship between the two variables.
Structure of a Two-Way Frequency Table
A two-way frequency table has rows representing the categories of one variable and columns representing the categories of another variable. Each cell in the table contains the count (frequency) of observations that fall into the corresponding row and column categories.
Applications of Relative Marginal Frequency
Various application of Relative Marginal Frequency includes:
- Sales Analysis: Companies analyze the relative marginal frequency of sales across different regions, product lines, or time periods to identify trends and optimize inventory and marketing efforts.
- Disease Prevalence: Public health officials use relative marginal frequencies to determine the proportion of the population affected by different diseases. This helps in allocating resources and planning interventions.
- Patient Demographics: Hospitals analyze the relative marginal frequency of patient visits across different departments, age groups, or conditions to improve service delivery and resource management.
- Performance Analysis: Educators use relative marginal frequencies to analyze student performance across different subjects, grades, or demographic groups. This helps in identifying areas that need improvement and implementing targeted educational programs.
- Resource Allocation: Schools and universities use relative marginal frequencies to allocate resources effectively, such as deciding the number of teachers needed for different subjects based on student enrollment proportions.
- Survey Analysis: Researchers use relative marginal frequencies to analyze survey data and understand the distribution of responses across different demographic groups or questions. This helps in drawing conclusions and making policy recommendations.
- Customer Behavior: E-commerce platforms analyze relative marginal frequencies of customer interactions, such as clicks, purchases, and returns, to improve user experience and personalize recommendations.
- Risk Assessment: Financial analysts use relative marginal frequencies to assess the proportion of different types of risks in a portfolio, aiding in risk management and investment decisions.
Read More:
Example 1: There are 16 students in a class, 6 boys and 10 girls. Find out the frequency as well as the relative frequency of boys?
Solution:
Frequency of boys (f) = total number of boys = 6
For relative frequency, we will use the general formula of the relative frequency = fn
Relative frequency = Boys Count / Total Student Count
= 6/16 = 0.375 = 37.5%
We can express relative frequency both as a fraction 6/16 and a percentage 37.5%.
Example 2: A cubical die is tossed 3030 times and lands 55 times on the number 66. What is the relative frequency of observing the die land on the number 66?
Solution:
Given, number of times a die is tossed = 30
Number of the successful trials of getting number ‘6’ = 8
By formula, we know,
Relative Frequency = (Number of Positive Trial) /(Total Number of Trials)
f = 5/30 = 16.66%
Hence, the relative frequency of observing the die land on the number 6 is 16.66%.
Example 3: A survey is made among 100 students in a middle school. They are asked, how they travel to school. The table given below shows the results of the survey.
|
|
CAR
|
BUS
|
OTHER TRANSPORT
|
TOTAL
|
|
GIRL
|
22
|
38
|
40
|
100
|
|
BOY
|
25
|
34
|
41
|
100
|
|
TOTAL
|
47
|
72
|
81
|
200
|
Use the above table to find each conditional relative frequency.
(i) Find the marginal relative frequency of the students who prefer car.
(ii) Find the marginal relative frequency of boys.
(iii) Find the marginal relative frequency of girls.
(iv) Find the marginal relative frequency of the students who prefer bus.
Solution (i):
Divide the total number of students who prefer car by the grand total.
Express your answer as a decimal and as a percent.
47/200 ≈ 0.24
= 24%
Solution (ii):
Divide the total number of boys by the grand total.
Express your answer as a decimal and as a percent.
100/200 = 0.50
= 50%
Solution (iii):
Divide the total number of girls by the grand total.
Express your answer as a decimal and as a percent.
100/200 = 0.50
= 50%
Solution (iv):
Divide the total number of students who prefer bus by the grand total.
Express your answer as a decimal and as a percent.
72/200 = 0.36
= 36%
FAQs Relative Marginal Frequency
What is Relative Marginal Frequency?
Relative marginal frequency is a measure in statistics that compares the frequency of a particular category or value to the total number of observations. It is expressed as a proportion or percentage of the total frequency.
How is Relative Marginal Frequency Calculated?
Relative marginal frequency is calculated using the formula:
Relative Marginal Frequency =Frequency of a particular categories /Total frequency of all categories
Why is Relative Marginal Frequency Important?
Relative marginal frequency provides insights into the distribution of data across different categories, making it easier to compare the relative importance or occurrence of each category within the dataset.
Can Relative Marginal Frequency Be Greater than 1?
No, relative marginal frequency is a proportion and will always range between 0 and 1, or between 0% and 100% when expressed as a percentage.
What Are Some Applications of Relative Marginal Frequency?
Relative marginal frequency is used in various fields such as market research, biology, social sciences, and economics to analyze and interpret categorical data. It helps in understanding patterns, trends, and relationships within the data.
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