# Calculate Data Points to Match Given Totals

• MHB
• micromichele
In summary, the conversation discusses a tricky problem involving different data sets with varying numbers. Each number is multiplied by 4.86 and rounded down, and then the total is added. However, the sum of the data points may also be multiplied by 4.86 and rounded down. The conversation notes that these operations do not always commute, meaning that the results of rounding down and then adding may not match the result of adding and then rounding down. The conversation suggests not rounding intermediate results and only rounding final results for display.
micromichele
Hello! I have a super tricky problem for everyone I truly hope there is an answer to this.

I have different data sets all of which are a different amount of number per set (total points per set)
Each number is multiplied by 4.86 then rounded down. Then the total is added

Alternatively the sum of the data points is multiplied by 4.86 then rounded down.

Just to add another note in case it was confusing so first set
189 needs to be 184
second set
2906 needs to be 2903
third
1219 needs to be 1215
fourth
102 needs to be 101

I need these two numbers to match and I can not figure out how I have attached a photo to help with this.

Let's denote the result of rounding down $x$ by $\lfloor x\rfloor$. This operation and addition do not commute, which means that in general $\lfloor x_1+x_2\rfloor\ne\lfloor x_1\rfloor+\lfloor x_2\rfloor$. One can only guarantee that $\lfloor x_1+x_2\rfloor\ge\lfloor x_1\rfloor+\lfloor x_2\rfloor$. The same holds for more than two numbers. Here $x_i$ denote the numbers from you datasets multiplied by 4.86. Therefore your mismatches are expected (provided the computations are correct), and you cannot make the results to coincide any more than you can make 2 + 2 equal 5.

A possible solution is to not round down.
It is good practice to never round intermediate results. And final results are usually rounded to appropriate precision only for display.
In Excel you can format fields to show data with a desired precision while the calculations still work with unrounded numbers.

Thank you for you replies and help :)

## 1. What is the purpose of calculating data points to match given totals?

The purpose of calculating data points to match given totals is to accurately represent and analyze data. By calculating data points, we can determine the relationships and patterns within the data, and make informed decisions based on the results.

## 2. How do you calculate data points to match given totals?

To calculate data points to match given totals, you need to have the total value and the number of data points you want to calculate. Then, you can use a mathematical formula or statistical method, such as linear regression or least squares, to determine the values of the data points that will add up to the given total.

## 3. What factors can affect the accuracy of calculated data points?

There are several factors that can affect the accuracy of calculated data points. These include the quality and completeness of the data, the chosen method for calculating the data points, and any assumptions made during the calculation process.

## 4. What are some common applications of calculating data points to match given totals?

Calculating data points to match given totals is commonly used in various fields, such as finance, economics, and science. It can be used to forecast future trends, analyze market data, and make predictions based on existing data.

## 5. Are there any limitations to calculating data points to match given totals?

Yes, there are limitations to calculating data points to match given totals. The accuracy of the results depends on the quality and completeness of the data, and the chosen method may not be suitable for all types of data. Additionally, the calculated data points may not always accurately represent the entire data set, and there may be other factors that influence the data that are not accounted for in the calculation.

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