Module 5 - SUMPRODUCT Theory - 1

Transcription

1 Module 5 - SUMPRODUCT Theory TOPICS COVERED: 1) Conjunction Truth Table (0:42) 2) Using the SUM Function to Count Records (2:20) 3) SUMPRODUCT Can Do the Same Thing (6:01) 4) Sumproduct Multiplication = Logical AND (9:50) 5) Sum of Products = SUMPRODUCT (11:35) 6) Totals vs. Counts (14:42) 7) Ferry Preferred Method (19:29) 8) SUMPRODUCT vs. SUMIFS, COUNTIFS, AVERAGEIFS (20:45) 9) Sumproduct Addition = Logical OR (25:05) When data mining for aggregate list metrics, such as totals and averages, the SUMPRODUCT function is one of Excel's most useful tools. Module 5 - SUMPRODUCT Theory - 1

2 Conjunction Truth Table (0:42) The conjunction truth table will be used to illustrate how SUMPRODUCT functions. Using the SUM Function to Count Records (2:20) Since Excel represents Boolean values TRUE and FALSE (1) SUM() can add boolean constants when entered as individual parameters. Excel returns a value of 3. (2) SUM() cannot be used to sum a range of Boolean values. Excel returns a value of 0. Module 5 - SUMPRODUCT Theory - 2

3 Arithmetic Operations to SUM Truth Table To get SUM() to work properly, we'll need to coerce each of the Boolean values into their numeric representations. We can achieve this by using the boolean in an arithmetic operation. (1) Some options for coercing the Boolean values: +0, *1, ^1, N() (2) The quickest (in terms of speed) is the unary operator, however, this makes the result a negative. (3) Use a double unary to maintain a positive result. It is faster than all of the other methods of arithmetic operations. SUMPRODUCT Can Do the Same Thing (6:01) SUMPRODUCT is an array funciton, and therefore, does not have to be array-entered. It produces an array formula that accepts arrays as input, but returns a single value. Nor does it not require the truth-table. SUMPRODUCT, like SUM, is not capable of summarizing a range of Booleans, so we must use the double unary. Sumproduct Multiplication = Logical AND (9:50) Module 5 - SUMPRODUCT Theory - 3

4 To compare more than one criteria, simply use multiplication in the SUMPRODUCT formula. In Boolean math, this equates to using the AND operator. Additionally, because of the multiplication operation, the double unary is no longer required. Module 5 - SUMPRODUCT Theory - 4

5 Sum of Products = SUMPRODUCT (11:35) (1) Each cell in the range E4:E23 is a formula that multiplies the corresponding truth table values in column A by column B. These are the "products". Module 5 - SUMPRODUCT Theory - 5

6 (2) The "sum" of those products is nothing more than the SUM of the range of the "Product" column. This is exactly how the SUMPRODUCT function works. It is the sum of products, although the truth table is calculated internally within the function. Totals & Inputs (14:42) When a total of records satisfying the comparison criteria is required then the criteria range is added without a boolean comparison. Module 5 - SUMPRODUCT Theory - 6

7 SUMPRODUCT does not require the truth table as it does all its calculations internally. SUMPRODUCT supports up to 30 input arrays separated by commas. In the examples above, all of the input criteria have been entered into the first array and using arithmetic operators. Thus, this method makes the number of input criteria essentially unlimited. Ferry Preferred Method (19:29) The preferred method for ease of construction and readability of SUMPRODUCT formulas is a combination method: (1) Group all boolean comparisons as criteria into the first input array. (2) Enter the totals criteria into the second input array. SUMPRODUCT vs. SUMIFS, COUNTIFS, AVERAGEIFS (20:45) Competing SUMPRODUCT formulas in versions of Excel since 2007: SUMIFS(), COUNTIFS(), AVERAGEIFS() They are somewhat faster than SUMPRODUCT. These functions all suffer from three problems: (1) They only work on newer versions of Excel. (2) Readability is not as easy as SUMPRODUCT (a bit subjective) (3) These functions are restricted to Logical AND operations. There is no way to get Logical OR functionality. Sumproduct Addition = Logical OR (25:05) Module 5 - SUMPRODUCT Theory - 7

8 The addition of the two boolean comparisons represents the logical OR operation. Module 5 - SUMPRODUCT Theory - 8