22. Excel data rounding

When data is compiled for a report or PowerPoint presentation, rounding summations in Excel is a frequent problem. It is often desirable, but difficult to achieve, that rounded totals exactly match the total of the rounded addends. For example, consider the following table:

When the values are rounded to integers using Excel’s Format-Cell function, the following table results. Totals which appear to be “miscalculated” are in bold:

Similarly, when Excel’s standard rounding functions are used, totals of the rounded values are calculated correctly but rounding errors accumulate and results often deviate substantially from the actual totals of the original values. The following table shows the result of =ROUND(x,0) for the example above. Totals that deviate from the original value by 1 or more are in bold:

Using think-cell round, you can achieve consistently rounded totals with minimal “cheating”: While most values are rounded to the nearest integer, a few values are rounded in the opposite direction, thus maintaining correct calculations without accumulating rounding error. Since there are many possibilities to achieve correctly rounded totals by changing values, the software picks a solution that requires the minimum number of values changed and the minimum deviation from the precise values. For example, rounding down 10.5 to 10 is preferable over rounding down 3.7 to 3. The following table shows an optimal solution for the above example, with “cheated” values in bold:

To achieve this output in your own calculation, simply select the concerned range of Excel cells. Then, click the button on the Formulas tab and, if necessary, adjust the rounding precision using the toolbar’s dropdown box.

22.1 22.1.1 Using think-cell round22.2 22.1.2 Limitations of think-cell round22.3 22.1.3 Troubleshooting TCROUND formulas

22.1 Using think-cell round

think-cell round seamlessly integrates into Microsoft Excel, providing a set of functions that are similar to Excel’s standard rounding functions. You can easily apply these functions to your own data using the think-cell round ribbon group in the Formulas tab.

22.1.1 Rounding parameters

Like the Excel functions, the think-cell rounding functions take two parameters:

x The value that is to be rounded. This can be a constant, a formula or a reference to another cell. n The rounding precision. The meaning of this parameter depends on the function you use. The parameters for the think-cell functions are the same as for the equivalent Excel functions. Refer to the table below for examples.

think-cell round can not only round to integer values, but to any multiple. For example, if you want to represent your data in 5-10-15-... steps, simply round to multiples of five. Using the dropdown box in the think-cell round toolbar, simply type in or select the desired rounding precision. think-cell round chooses the appropriate function and parameters for you. The following table provides some examples of rounding certain x-values using the toolbar together with their specific n-parameter.

x = n =	100	50	2	1	0.01
1.018	0	0	2	1	1.02
17	0	0	18	17	17.00
54.6	100	50	54	55	54.60
1234.1234	1200	1250	1234	1234	1234.12
8776.54321	8800	8800	8776	8777	8776.54

If the values are not displayed the way you expect them to, verify that the Excel Cell Formatting is set to General and the columns are wide enough to display all decimal places.

Button	Formula	Description
	TCROUND(x, n)	Let think-cell round decide to which of the two nearest multiples to round to minimize rounding error.
	TCROUNDUP(x, n)	Force rounding of x away from zero.
	TCROUNDDOWN(x, n)	Force rounding of x towards zero.
	TCROUNDNEAR(x, n)	Force rounding of x to the nearest multiple of the desired precision.
		Remove all think-cell round functions from the selected cells.
		Select or type the desired rounding multiple.
		Highlight all cells which think-cell decided to round to the farther of the two closest multiples instead of to the nearest.
		The turning wheel indicates that think-cell round is busy.

For optimal results with as little deviation from the underlying values as possible, you should use TCROUND wherever possible. Only use the more restrictive functions TCROUNDDOWN, TCROUNDUP or TCROUNDNEAR if you must.

Attention: You should never use nondeterministic functions like RAND() within any of the TCROUND formulas. If functions return a different value every time they are evaluated, think-cell round will make mistakes calculating values.

22.1.2 Layout of the calculation

The rectangular layout of the example above is only for sake of demonstration. You can use the TCROUND functions to determine the display of arbitrary summations spread across your Excel sheet. Excel’s 3-D references to other sheets and links to other files do also work.

22.1.3 Placement of TCROUND functions

Since TCROUND functions are meant to control the output of a cell, they must be the outermost function:

Bad:	=TCROUND(A1, 1)+TCROUND(SUM(B1:E1), 1)
Good:	=TCROUND(A1+SUM(B1:E1), 1)
Bad:	=3*TCROUNDDOWN(A1, 1)
Good:	=TCROUNDDOWN(3*A1, 1)

If you happen to enter something along the lines of the bad examples, think-cell round will notify you with the Excel error value #VALUE!.

22.2 Limitations of think-cell round

think-cell round always finds a solution for arbitrary summations with subtotals and totals. think-cell round also provides sensible solutions for some other calculations involving multiplication and numerical functions. However, for mathematical reasons, the existence of a consistently rounded solution cannot be guaranteed as soon as operators other than +, - and SUM are used.

22.2.1 Multiplication with a constant

In many cases, think-cell round produces good results when constant multiplication is involved, i.e., at most one of the coefficients is derived from the result of another TCROUND function. Consider the following example:

The precise calculation for cell C1 is 3×1.3+1.4=5.3. This result can be met by rounding up the value 1.4 to 2:

However, think-cell round can only “cheat” by rounding up or rounding down. Further deviation from the original values is not supported. Thus, for certain combinations of input values, no consistently rounded solution can be found. In this case, the function TCROUND evaluates to the Excel error value #NUM!. The following example illustrates an unsolvable problem:

The precise calculation for cell C1 is 6×1.3+1.4=9.2. Rounding cells A1 and B1 would result in 6×1+2=8 or 6×2+1=13. The actual result 9.2 cannot be rounded to 8 or 13, and the output from think-cell round looks like this:

Note: The Excel function AVERAGE is interpreted by think-cell round as a combination of summation and constant multiplication. Also, a summation where the same addend appears more than once is mathematically equivalent to a constant multiplication, and the existence of a solution is not guaranteed.

22.2.2 General multiplication and other functions

As long as the TCROUND functions are used for all relevant cells and intermediate results are connected merely by +, -, SUM and AVERAGE, the addends as well as (intermediate) totals are integrated into a single rounding problem. In these cases, think-cell round will find a solution that provides consistency throughout all cells involved, if such a solution exists.

Since TCROUND is a normal Excel function, it can be combined with arbitrary functions and operators. But when you use functions other than the ones mentioned above to connect results from TCROUND statements, think-cell round cannot integrate the components into one interconnected problem. Instead, the components of the formula will be taken as distinct problems which will be solved independently. The results will then be used as input to other formulas.

In many cases, the output from think-cell round will still be reasonable. There are cases, however, where the use of operators other than +, -, SUM and AVERAGE leads to rounded results which are far off from the result of the non-rounded calculation. Consider the following example:

In this case, the precise calculation for cell C1 would be 8.7×1.7=14.79. Since cell A1 and cell B1 are connected by a multiplication, think-cell round cannot integrate the formulas from these cells into a common problem. Instead, after detecting cell A1 as valid input, cell B1 is evaluated independently and the output is taken as a constant within the remaining problem. Since there are no further constraints, value 1.7 from cell B1 is rounded to the nearest integer, which is 2.

At this point, the “precise” calculation for cell C1 is 8.7×2=17.4. This is the problem that think-cell round now tries to solve. There is a consistent solution which requires rounding up 17.4 to 18. The result looks like this:

Note that the rounded value in cell C1, which is 18, greatly differs from the original value 14.79.

22.3 Troubleshooting TCROUND formulas

There are two possible error results you may come across when using think-cell round: #VALUE! and #NUM!.

22.3.1 #VALUE!

The #VALUE! error hints to syntactical problems, such as mistyped formulas or bad parameters. Also, pay attention to use correct delimiters: For example, while in international Excel the formula looks like this: =TCROUND(1.7, 0), in a localized German version of Excel it must be written as =TCROUND(1,7; 0).

Another mistake specific to think-cell round is the placement of the TCROUND function call: You cannot use a TCROUND function within another formula. Please make sure that TCROUND is the outermost function of the cell’s formula. (see Placement of TCROUND functions)

22.3.2 #NUM!

The #NUM! error results from numerical problems. When the output of a TCROUND function is #NUM!, this means that the problem as stated by the given set of formulas is mathematically unsolvable. (see 22.1.2 Limitations of think-cell round)

As long as the formulas enclosed by TCROUND functions contain merely +, - and SUM, and all TCROUND statements share the same precision (second parameter), a solution is guaranteed to exist and will be found by think-cell round. However, in the following cases there is no guarantee that a consistently rounded solution exists:

• Formulas involve other operations like multiplication or numerical functions. Also, summations where the same addend appears more than once are mathematically equivalent to a multiplication.
• You use different precisions in the second parameter of the TCROUND function.
• You make frequent use of the specific functions TCROUNDDOWN, TCROUNDUP and TCROUNDNEAR.

You can try to restate the problem to get a consistent solution. Try the following:

• Use a finer precision for some or all TCROUND statements.
• Do not use TCROUND with multiplication or numerical functions other than +, - and SUM.
• Use the same precision (second parameter) for all TCROUND statements.
• Use TCROUND instead of the more specific functions TCROUNDDOWN, TCROUNDUP and TCROUNDNEAR wherever possible.