What does it mean if a percentage is higher than Benford's law percentage. Can you give me a detailed explanation because I have been reading about it for the last hour and it is still kind of hard to grasp at the moment? The image I have attached is pertaining to sales revenue.
What does it mean if a percentage is higher than Benford's law percentage. Can you give me a detailed explanation because I have been reading about it for the last hour and it is still kind of hard to grasp at the moment? The image I have attached is pertaining to sales revenue.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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What does it mean if a percentage is higher than Benford's law percentage. Can you give me a detailed explanation because I have been reading about it for the last hour and it is still kind of hard to grasp at the moment? The image I have attached is pertaining to sales revenue.
![### First Number Distribution Table
The table below displays the distribution of the first digit of a dataset according to expected percentages and the actual percentage of the total. This is likely used to analyze the conformity of data to Benford's Law, which predicts the frequency distribution of the leading digits in many real-life sets of numerical data.
#### Table: Distribution of Leading Digits
| First Number | Expected % | Percent of Total |
|--------------|-------------|------------------|
| 0 | – | +0.00 % |
| 1 | 30.10 % | 36.67 % |
| 2 | 17.60 % | 18.79 % |
| 3 | 12.50 % | 13.47 % |
| 4 | 9.60 % | 7.94 % |
| 5 | 7.90 % | 5.72 % |
| 6 | 6.70 % | 4.82 % |
| 7 | 5.80 % | 4.10 % |
| 8 | 5.10 % | 3.95 % |
| 9 | 4.60 % | 4.53 % |
#### Explanation of the Table
1. **First Number**: This column indicates the leading digit of the numbers in the dataset under analysis.
2. **Expected %**: This column shows the expected percentage distribution of each leading digit according to Benford's Law.
3. **Percent of Total**: This column displays the actual percentage observed in the dataset for each leading digit.
#### Observations
- The leading digit '1' is expected to appear 30.10% of the time but appears 36.67% in the actual dataset.
- The leading digit '2' appears 18.79% in the dataset compared to the expected 17.60%.
- There is a noticeable difference in the numbers, particularly where some actual percentages exceed or fall short of the expected percentage distribution.
#### Conclusion
Analyzing the distribution of leading digits can be crucial for understanding patterns in datasets and can be used in fields such as fraud detection and forensic accounting. This table exemplifies a typical comparison of expected versus actual distributions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3407f286-e923-417c-9ab2-bf214e17bc12%2F0f1c1658-8989-419f-9f7d-2e3c5a1274c3%2F7l573wd_processed.png&w=3840&q=75)
Transcribed Image Text:### First Number Distribution Table
The table below displays the distribution of the first digit of a dataset according to expected percentages and the actual percentage of the total. This is likely used to analyze the conformity of data to Benford's Law, which predicts the frequency distribution of the leading digits in many real-life sets of numerical data.
#### Table: Distribution of Leading Digits
| First Number | Expected % | Percent of Total |
|--------------|-------------|------------------|
| 0 | – | +0.00 % |
| 1 | 30.10 % | 36.67 % |
| 2 | 17.60 % | 18.79 % |
| 3 | 12.50 % | 13.47 % |
| 4 | 9.60 % | 7.94 % |
| 5 | 7.90 % | 5.72 % |
| 6 | 6.70 % | 4.82 % |
| 7 | 5.80 % | 4.10 % |
| 8 | 5.10 % | 3.95 % |
| 9 | 4.60 % | 4.53 % |
#### Explanation of the Table
1. **First Number**: This column indicates the leading digit of the numbers in the dataset under analysis.
2. **Expected %**: This column shows the expected percentage distribution of each leading digit according to Benford's Law.
3. **Percent of Total**: This column displays the actual percentage observed in the dataset for each leading digit.
#### Observations
- The leading digit '1' is expected to appear 30.10% of the time but appears 36.67% in the actual dataset.
- The leading digit '2' appears 18.79% in the dataset compared to the expected 17.60%.
- There is a noticeable difference in the numbers, particularly where some actual percentages exceed or fall short of the expected percentage distribution.
#### Conclusion
Analyzing the distribution of leading digits can be crucial for understanding patterns in datasets and can be used in fields such as fraud detection and forensic accounting. This table exemplifies a typical comparison of expected versus actual distributions.
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