Counting the total number of cells

To get a count of the total number of cells in a range, use the following formula. This formula returns the number of cells in a range named Data. It simply multiplies the number of rows (returned by the ROWS function) by the number of columns (returned by the COLUMNS function).

=ROWS(Data)*COLUMNS(Data)

Counting blank cells

The following formula returns the number of blank (empty) cells in a range named Data:

=COUNTBLANK(Data)

This function works only with a contiguous range of cells. If Data is defined as a noncontiguous range, the function returns a #VALUE! error.

The COUNTBLANK function also counts cells containing a formula that returns an empty string. For example, the formula that follows returns an empty string if the value in cell A1 is greater than 5. If the cell meets this condition, the COUNTBLANK function counts that cell:

=IF(A1>5,"",A1)

You can use the COUNTBLANK function with an argument that consists of entire rows or columns. For example, this next formula returns the number of blank cells in column A:

=COUNTBLANK(A:A)

The following formula returns the number of empty cells on the entire worksheet named Sheet1. You must enter this formula on a sheet other than Sheet1, or it will create a circular reference.

=COUNTBLANK(Sheet1!1:1048576)

Counting nonblank cells

The following formula uses the COUNTA function to return the number of nonblank cells in a range named Data:

=COUNTA(Data)

The COUNTA function counts cells that contain values, text, or logical values (TRUE or FALSE).

Counting numeric cells

To count only the numeric cells in a range, use the following formula, which assumes that the range is named Data:

=COUNT(Data)

Cells that contain a date or a time are considered to be numeric cells. Cells that contain a logical value (TRUE or FALSE) are not considered to be numeric cells.

Counting text cells

To count the number of text cells in a range, you need to use an array formula. The array formula that follows returns the number of text cells in a range named Data:

{=SUM(IF(ISTEXT(Data),1))}

Counting nontext cells

The following array formula uses Excel’s ISNONTEXT function, which returns TRUE if its argument refers to any nontext cell (including a blank cell). This formula returns the count of the number of cells not containing text (including blank cells):

{=SUM(IF(ISNONTEXT(Data),1))}

Counting logical values

The following array formula returns the number of logical values (TRUE or FALSE) in a range named Data:

{=SUM(IF(ISLOGICAL(Data),1))}

Counting error values in a range

Excel has three functions that help you determine whether a cell contains an error value:

• ISERROR: Returns TRUE if the cell contains any error value (#N/A, #VALUE!, #REF!, #DIV/0!, #NUM!, #NAME?, or #NULL!)
• ISERR: Returns TRUE if the cell contains any error value except #N/A
• ISNA: Returns TRUE if the cell contains the #N/A error value

You can use these functions in an array formula to count the number of error values in a range. The following array formula, for example, returns the total number of error values in a range named Data:

{=SUM(IF(ISERROR(Data),1))}

Depending on your needs, you can use the ISERR or ISNA function in place of ISERROR.

If you need to count specific types of errors, you can use the COUNTIF function. The following formula, for example, returns the number of #DIV/0! error values in the range named Data:

=COUNTIF(Data,"#DIV/0!")

Note that the COUNTIF function works only with a contiguous range argument. If Data is defined a noncontiguous range, the formula returns a #VALUE! error.

Counting cells with the COUNTIF function

Excel’s COUNTIF function is useful for single-criterion counting formulas. The COUNTIF function takes two arguments:

• range: The range that contains the values that determine whether to include a particular cell in the count
• criteria: The logical criteria that determine whether to include a particular cell in the count

Table 7.2 contains several examples of formulas that use the COUNTIF function. All these formulas work with a range named Data. As you can see, the criteria argument is quite flexible. You can use constants, expressions, functions, cell references, and even wildcard characters (* and ?).

Counting cells that meet multiple criteria

In many cases, your counting formula will need to count cells only if two or more criteria are met. These criteria can be based on the cells that are being counted or based on a range of corresponding cells.

Figure 7.2 shows a simple worksheet that we use for the examples in this section. This sheet shows sales figures (Amount) categorized by Month, SalesRep, and Type. The worksheet contains named ranges that correspond to the labels in row 1.

=COUNTIFS(Amount,">100",Amount,"<=200")

=COUNTIF(Amount,">100")-COUNTIF(Amount,">200")

{=SUM((Amount>100)*(Amount<=200))}

=COUNTIFS(Month,"January",SalesRep,"Brooks",Amount,">1000")

=SUMPRODUCT((Month="January")*(SalesRep="Brooks")*(Amount>1000))

{=SUM((Month="January")*(SalesRep="Brooks")*(Amount>1000))}

=COUNTIF(Month,"January")+COUNTIF(Month,"February")

{=SUM(COUNTIF(Month,{"January","February"}))}

{=SUM(IF((Month="January")+(SalesRep="Brooks")+(Amount>1000),1))}

=COUNTIFS(Month,"January",SalesRep,"Brooks")+
COUNTIFS(Month,"January",SalesRep,"Cook")

{=SUM((Month="January")*((SalesRep="Brooks")+(SalesRep="Cook")))}

Counting the most frequently occurring entry

Excel’s MODE function returns the most frequently occurring value in a range. Figure 7.3 shows a worksheet with values in range A1:A9 (named Data). The formula that follows returns 10 because that value appears most frequently in the Data range:

=MODE(Data)

The formula returns an #N/A error if the Data range contains no duplicated values.

To count the number of times the most frequently occurring value appears in the range—in other words, the frequency of the mode—use the following formula:

=COUNTIF(Data,MODE(Data))

This formula returns 3 because the modal value (10) appears three times in the Data range.

The MODE function works only for numeric values, and it ignores cells that contain text. To find the most frequently occurring text entry in a range, you need to use an array formula.

To count the number of times the most frequently occurring item (text or values) appears in a range named Data, use the following array formula:

{=MAX(COUNTIF(Data,Data))}

This next array formula operates like the MODE function except that it works with both text and values:

{=INDEX(Data,MATCH(MAX(COUNTIF(Data,Data)),COUNTIF(Data,Data),0))}

Counting the occurrences of specific text

The examples in this section demonstrate various ways to count the occurrences of a character or text string in a range of cells. Figure 7.4 shows a worksheet that demonstrates these examples. Various text appears in the range A1:A10 (named Data); cell B1 is named Text.

=COUNTIF(Data,Text)

{=SUM(IF(EXACT(Data,Text),1))}

=COUNTIF(Data,"*"&Text&"*")

{=SUM(IF(NOT(ISERROR(SEARCH(text,data))),1))}

{=SUM(IF(LEN(Data)-LEN(SUBSTITUTE(Data,Text,""))>0,1))}

{=SUM(IF(NOT(ISERROR(FIND(text,data))),1))}

{=(SUM(LEN(Data))-SUM(LEN(SUBSTITUTE(Data,Text,""))))/LEN(Text)}

{=(SUM(LEN(Data))-SUM(LEN(SUBSTITUTE(UPPER(Data),UPPER(Text),""))))/LEN(Text)}

Counting the number of unique values

The following array formula returns the number of unique values in a range named Data:

{=SUM(1/COUNTIF(Data,Data))}

To understand how this formula works, you need a basic understanding of array formulas. (See Chapter 14 for an introduction to this topic.) In Figure 7.5, range A1:A12 is named Data. Range C1:C12 contains the following multicell array formula. A single formula was entered into all 12 cells in the range:

{=COUNTIF(Data,Data)}

The array in range C1:C12 consists of the count of each value in Data. For example, the number 125 appears three times, so each array element that corresponds to a value of 125 in the Data range has a value of 3.

Range D1:D12 contains the following array formula:

{=1/C1:C12}

This array consists of each value in the array in range C1:C12, divided into 1. For example, each cell in the original Data range that contains a 200 has a value of 0.5 in the corresponding cell in D1:D12.

Summing the range D1:D12 gives the number of unique items in Data. The array formula presented at the beginning of this section essentially creates the array that occupies D1:D12 and sums the values.

This formula has a serious limitation: if the range contains any blank cells, it returns an error. The following array formula solves this problem:

{=SUM(IF(COUNTIF(Data,Data)=0,"",1/COUNTIF(Data,Data)))}

Creating a frequency distribution

A frequency distribution basically comprises a summary table that shows the frequency of each value in a range. For example, an instructor may create a frequency distribution of test scores. The table would show the count of As, Bs, Cs, and so on. Excel provides a number of ways to create frequency distributions. You can

• Use the FREQUENCY function.
• Create your own formulas.
• Use the Analysis ToolPak add-in.
• Use a pivot table.

The FREQUENCY function

The first method that we discuss uses the FREQUENCY function. This function always returns an array, so you must use it in an array formula entered into a multicell range.

Figure 7.6 shows some data in range A1:E25 (named Data). These values range from 1 to 500. The range G2:G11 contains the bins used for the frequency distribution. Each cell in this bin range contains the upper limit for the bin. In this case, the bins consist of <=50, 51–100, 101–150, and so on. See the sidebar, “Creating bins for a frequency distribution,” to discover an easy way to create a bin range.

To create the frequency distribution, select a range of cells that corresponds to the number of cells in the bin range. Then enter the following array formula in H2:H11:

{=FREQUENCY(Data,G2:G11)}

The array formula enters the count of values in the Data range that fall into each bin. To create a frequency distribution that consists of percentages, use the following array formula:

{=FREQUENCY(Data,G2:G11)/COUNT(Data)}

Figure 7.7 shows two frequency distributions—one in terms of counts, and one in terms of percentages. The figure also shows a chart (histogram) created from the frequency distribution.

Using formulas to create a frequency distribution

Figure 7.8 shows a worksheet that contains test scores for 50 students in column B. (The range is named Grades.) Formulas in columns G and H calculate a frequency distribution for letter grades. The minimum and maximum values for each letter grade appear in columns D and E. For example, a test score between 80 and 89 (inclusive) qualifies for a B.

The formula in cell G2 that follows is an array formula that counts the number of scores that qualify for an A:

{=SUM((Grades>=D2)*(Grades<=E2))}

You may recognize this formula from a previous section in this chapter. (See “Counting cells that meet multiple criteria.”) This formula was copied to the four cells below G2.

The formulas in column H calculate the percentage of scores for each letter grade. The formula in H2, which was copied to the four cells below H2, is

=G2/SUM($G$2:$G$6)

Using the Analysis ToolPak to create a frequency distribution

After you install the Analysis ToolPak add-in, you can use the Histogram option to create a frequency distribution. Start by entering your bin values in a range. Then choose Data ➜ Analysis ➜ Data Analysis to display the Data Analysis dialog box. Next, select Histogram and click OK. You should see the Histogram dialog box shown in Figure 7.9.

Specify the ranges for your data (Input Range), bins (Bin Range), and results (Output Range), and then select any options. Figure 7.10 shows a frequency distribution (and chart) created with the Histogram option.

Using a pivot table to create a frequency distribution

If your data is in the form of a table, you may prefer to use a pivot table to create a histogram. Figure 7.11 shows the student grade data summarized in a pivot table and a pivot chart.

Using adjustable bins to create a histogram

Figure 7.12 shows a worksheet with student grades listed in column B (67 students total). Columns D and E contain formulas that calculate the upper and lower limits for bins, based on the entry in cell E1 (named BinSize). For example, if BinSize is 12 (as in the figure), then each bin contains 12 scores (1–12, 13–24, and so on).

The chart uses two dynamic names in its SERIES formula. You can define the name Categories with the following formula:

=OFFSET(Sheet1!$E$4,0,0,ROUNDUP(100/BinSize,0))

You can define the name Frequencies with this formula:

=OFFSET(Sheet1!$F$4,0,0,ROUNDUP(100/BinSize,0))

The net effect is that the chart adjusts automatically when you change the BinSize cell.

Summing all cells in a range

It doesn’t get much simpler than this. The following formula returns the sum of all values in a range named Data:

=SUM(Data)

The SUM function can take up to 255 arguments. The following formula, for example, returns the sum of the values in five noncontiguous ranges:

=SUM(A1:A9,C1:C9,E1:E9,G1:G9,I1:I9)

You can use complete rows or columns as an argument for the SUM function. The formula that follows, for example, returns the sum of all values in column A. If this formula appears in a cell in column A, it generates a circular reference error.

=SUM(A:A)

The following formula returns the sum of all values on Sheet1. To avoid a circular reference error, this formula must appear on a sheet other than Sheet1.

=SUM(Sheet1!1:1048576)

The SUM function is versatile. The arguments can be numerical values, cells, ranges, text representations of numbers (which are interpreted as values), logical values, array constants, and even embedded functions. For example, consider the following formula:

=SUM(B1,5,"6",,SQRT(4),{1,2,3},A1:A5,TRUE)

This formula, which is a perfectly valid formula, contains all the following types of arguments, listed here in the order of their presentation:

• A single cell reference
• A literal value
• A string that looks like a value
• A missing argument
• An expression that uses another function
• An array constant
• A range reference
• A logical TRUE value

Summing a range that contains errors

The SUM function does not work if the range to be summed includes errors. For example, if one of the cells to be summed displays #N/A, the SUM function will also return #N/A.

To add the values in a range and ignore the error cells, use the AGGREGATE function. For example, to sum a range named Data (which may have error values), use this formula:

=AGGREGATE(9,6,Data)

The AGGREGATE function is versatile and can do a lot more than just add values. In this example, the first argument (9) specifies SUM. The second argument (6) means to ignore error values.

The arguments are described in the Excel Help. Excel also provides good autocomplete assistance when you enter a formula that uses this function.

Computing a cumulative sum

You may want to display a cumulative sum of values in a range—sometimes known as a running total. Figure 7.13 illustrates a cumulative sum. Column B shows the monthly amounts, and column C displays the cumulative (year-to-date) totals.

The formula in cell C2 is

=SUM(B$2:B2)

Notice that this formula uses a mixed reference. The first cell in the range reference always refers to the same row: in this case, row 2. When this formula is copied down the column, the range argument adjusts so that the sum always starts with row 2 and ends with the current row. For example, after copying this formula down column C, the formula in cell C8 is

=SUM(B$2:B8)

You can use an IF function to hide the cumulative sums for rows in which data hasn’t been entered. The following formula, entered in cell C2 and copied down the column, is

=IF(ISBLANK(B2),"",SUM(B$2:B2))

Figure 7.14 shows this formula at work.

Summing the “top n” values

In some situations, you may need to sum the n largest values in a range—for example, the top 10 values. If your data resides in a table, you can use AutoFilter to hide all but the top n rows and then display the sum of the visible data in the table’s Total row.

Another approach is to sort the range in descending order and then use the SUM function with an argument consisting of the first n values in the sorted range.

A better solution—which doesn’t require a table or sorting—uses an array formula like this one:

{=SUM(LARGE(Data,{1,2,3,4,5,6,7,8,9,10}))}

This formula sums the 10 largest values in a range named Data. To sum the 10 smallest values, use the SMALL function instead of the LARGE function:

{=SUM(SMALL(Data,{1,2,3,4,5,6,7,8,9,10}))}

These formulas use an array constant comprising the arguments for the LARGE or SMALL function. If the value of n for your top-n calculation is large, you may prefer to use the following variation. This formula returns the sum of the top 30 values in the Data range. You can, of course, substitute a different value for 30. Figure 7.15 shows this array formula in use:

{=SUM(LARGE(Data,ROW(INDIRECT("1:30"))))}

Summing only negative values

The following formula returns the sum of the negative values in column F. In other words, it returns the total number of past-due days for all invoices. For this worksheet, the formula returns –63:

=SUMIF(Difference,"<0")

Because you omit the third argument, the second argument ("<0") applies to the values in the Difference range.

You do not need to hard-code the arguments for the SUMIF function into your formula. For example, you can create a formula such as the following, which gets the criteria argument from the contents of cell G2:

=SUMIF(Difference,G2)

This formula returns a new result if you change the criteria in cell G2.

Summing values based on a different range

The following formula returns the sum of the past-due invoice amounts (see column C in Figure 7.16):

=SUMIF(Difference,"<0",Amount)

This formula uses the values in the Difference range to determine whether the corresponding values in the Amount range contribute to the sum.

Summing values based on a text comparison

The following formula returns the total invoice amounts for the Oregon office:

=SUMIF(Office,"=Oregon",Amount)

Using the equal sign is optional. The following formula has the same result:

=SUMIF(Office,"Oregon",Amount)

To sum the invoice amounts for all offices except Oregon, use this formula:

=SUMIF(Office,"<>Oregon",Amount)

Text comparisons are not case sensitive.

Summing values based on a date comparison

The following formula returns the total invoice amounts that have a due date after May 1, 2013:

=SUMIF(DateDue,">="&DATE(2013,5,1),Amount)

Notice that the second argument for the SUMIF function is an expression. The expression uses the DATE function, which returns a date. Also, the comparison operator, enclosed in quotation marks, is concatenated (using the & operator) with the result of the DATE function.

The formula that follows returns the total invoice amounts that have a future due date (including today):

=SUMIF(DateDue,">="&TODAY(),Amount)

Using And criteria

Suppose you want to get a sum of both the invoice amounts that are past due as well as associated with the Oregon office. In other words, the value in the Amount range will be summed only if both of the following criteria are met:

• The corresponding value in the Difference range is negative.
• The corresponding text in the Office range is Oregon.

The SUMIFS function was designed for just this task:

=SUMIFS(Amount,Difference,"<0",Office,"Oregon")

For use with versions prior to Excel 2007, the following array formula also does the job:

{=SUM((Difference<0)*(Office="Oregon")*Amount)}

This formula creates two new arrays (in memory):

• A Boolean array that consists of TRUE if the corresponding Difference value is less than zero; FALSE otherwise
• A Boolean array that consists of TRUE if the corresponding Office value equals Oregon; FALSE otherwise

Multiplying Boolean values result in the following:

• TRUE * TRUE = 1
• TRUE * FALSE = 0
• FALSE * FALSE = 0

Therefore, the corresponding Amount value returns nonzero only if both the corresponding values in the memory arrays are TRUE. The result produces a sum of the Amount values that meet the specified criteria.

Using Or criteria

Suppose you want to get a sum of past-due invoice amounts, or ones associated with the Oregon office. In other words, the value in the Amount range will be summed if either of the following criteria is met:

• The corresponding value in the Difference range is negative.
• The corresponding text in the Office range is Oregon.

The following array formula does the job:

{=SUM(IF((Office="Oregon")+(Difference<0),1,0)*Amount)}

A plus sign (+) joins the conditions; you can include more than two conditions.

Using And and Or criteria

As you might expect, things get a bit tricky when your criteria consists of both And and Or operations. For example, you may want to sum the values in the Amount range when both of the following conditions are met:

• The corresponding value in the Difference range is negative.
• The corresponding text in the Office range is Oregon or California.

Notice that the second condition actually consists of two conditions, joined with Or. Using multiple SUMIFS can accomplish this:

=SUMIFS(Amount,Difference,"<0",Office,"Oregon")
+SUMIFS(Amount,Difference,"<0",Office,"California")

The following array formula also does the trick:

{=SUM((Difference<0)*((Office="Oregon")+(Office="California"))*(Amount))}