# Help in identifying why these two calculations have the same result?

• MHB
• BTH
In summary, the conversation is about a person noticing that they are getting the same result from different calculations on a data-set. They provide a simplified scenario where a group of 10 people are asked to eat at least 1 apple each day for 5 days. The researcher looks at the data to determine the percentage of people who met the goal each day and the total number of apples eaten by each person over the 5 day period. The person then explains that when they sum the percentage of people who ate an apple each day and average the total number of apples eaten, the results are the same. They conclude that this is because the numbers are divided by 100 in decimal form and the same operations are being used.
BTH
Hi All,

This may not be the correct sub-forum in which to post this question and probably a very simple question, so I apologize in advance. I was analyzing some data for a project and noticed I was getting the same result from different calculations on the data-set and am very curious as to why! I've restated the scenario in a simplified example and am hoping someone with more of a math background than me can provide the mathematical explanation.

Scenario: A group of 10 people are asked to attempt eating at least 1 apple each day for 5 days. At the end of 5 days, the researcher looks at the data to determine what percentage of the group met the goal each day, as well as the total number of apples eaten by each test subject over the 5 day period. When I sum the % of total test subjects who ate an apple each day and also average the total number of apples eaten over the week by all subjects, the results are the same. The calculated data is pasted below.

View attachment 7677

#### Attachments

• Apple example.PNG
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You're summing the second-last row and then dividing by 10. With the last row we note that percentages are actually in decimal form, i.e. divided by 100 (e.g. 90/100 = 9/10) and then these numbers are summed. Same operations, same numbers = same numbers, same operations.

## 1. Why do these two calculations have the same result?

This could be due to various factors, such as using the same formula or algorithm, rounding errors, or inputting the same values. It is important to carefully review the calculations and their inputs to determine the exact reason.

## 2. How can I identify the cause of the same result in two calculations?

To identify the cause, you can compare the formulas or algorithms used, check for any rounding errors, and thoroughly review the input values for any duplicates or similarities.

## 3. Is it possible for two different calculations to have the same result?

Yes, it is possible for two different calculations to have the same result. This can occur if the calculations have similar inputs or if there is a mistake in one of the calculations.

## 4. What should I do if I suspect an error in one of the calculations?

If you suspect an error, it is important to carefully review the calculation and its inputs for any mistakes. You can also consult with a colleague or another expert in the field to get a second opinion.

## 5. Can the same result in two calculations be a coincidence?

While it is possible, it is unlikely for two calculations to have the exact same result by coincidence. It is important to carefully review the calculations and their inputs to determine the cause of the same result.

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