259 Lecture 4 Spring 2010 Logical Functions and Conditional Formatting in Excel

2 Logical Functions  Excel’s built-in logical functions are useful for introducing conditional statements, i.e. “decision making” functions into a spreadsheet!  The functions are:  TRUE  FALSE  NOT  AND  OR  IF  IFERROR (new in Excel 2007)  Information on each of these functions can be found in the Help File or at Microsoft’s Office Web pages:

3 The TRUE Function  Syntax: TRUE( )  Returns the logical value TRUE.  TRUE can be entered directly into cells and formulas without using this function.

4 The FALSE Function  Syntax: FALSE( )  Returns the logical value FALSE.  FALSE can be entered directly into cells and formulas without using this function.

5 The NOT Function  Syntax: NOT(logical)  logical is a value or expression that can be evaluated to TRUE or FALSE.  Reverses the logical value of its argument.  If logical is FALSE, NOT returns TRUE.  If logical is TRUE, NOT returns FALSE.

6 Example 1  Try NOT on the following: 0, 1, a, FALSE, 1+1=2.

7 Example 1 (cont.)

8 The AND Function  Syntax: AND(logical1,logical2,...)  logical1, logical2,... are 1 to 255 conditions you want to test that can be either TRUE or FALSE.  Returns TRUE if all its arguments are TRUE.  Returns FALSE if one or more argument is FALSE.

9 The AND function (cont.)  The arguments must evaluate to logical values such as TRUE or FALSE, or the arguments must be arrays (i.e. rectangular blocks of cells) or references that contain logical values.  If an array or reference argument contains text or empty cells, those values are ignored.  If the specified range contains no logical values, AND returns the #VALUE! error value.

10 Example 2  Make an AND truth table in Excel! ANDTRUEFALSE TRUE FALSE

Example 2 (cont.) 11

12 The OR Function  Syntax: OR(logical1,logical2,...)  logical1, logical2,... are 1 to 255 conditions you want to test that can be either TRUE or FALSE.  Returns TRUE if any argument is TRUE.  Returns FALSE if all arguments are FALSE.

13 The OR Function (cont.)  The arguments must evaluate to logical values such as TRUE or FALSE, or the arguments must be arrays or references that contain logical values.  If an array or reference argument contains text or empty cells, those values are ignored.  If the specified range contains no logical values, OR returns the #VALUE! error value.

14 Example 3  Make an OR truth table in Excel! ORTRUEFALSE TRUE FALSETRUEFALSE

Example 3 (cont.) 15

16 The IF function  Syntax: IF(logical_test,value_if_true,value_if_false)  logical_test is any value or expression that can be evaluated to TRUE or FALSE.  value_if_true is the value that is returned if logical_test is TRUE.  value_if_false is the value that is returned if logical_test is FALSE.

17 Example 4  Try each of the following IF statements: 1.=IF(1 < 2, “Mickey Mouse”, “Donald Duck”) 2.=IF(1 > 2, “Mickey Mouse”, “Donald Duck”) 3.=IF(1 <= 2,) 4.=IF(1 <> 2, TRUE) 5.=IF(1 < 2, 6*2+5) 6.=IF(1 >= 2,) 7.=IF(1 > 2, TRUE) 8.=IF(“yes” = “no”, 6*2+5, 2-10^3)

18 Example 4 (cont.)

19 The IF function (cont.)  If logical_test is TRUE and value_if_true is blank, this argument returns 0 (zero).  To display the word TRUE, use the logical value TRUE for value_if_true.  value_if_true can be another formula.  If logical_test is FALSE and value_if_false is omitted, (that is, after value_if_true, there is no comma), then the logical value FALSE is returned.  If logical_test is FALSE and value_if_false is blank (that is, after value_if_true, there is a comma followed by the closing parenthesis), then the value 0 (zero) is returned.  value_if_false can be another formula.

20 Example 5  Use IF to create a piecewise-defined function for the absolute value function.

21 Example 6  Use IF to assign grades automatically in a grade book!  If score ≥ 93, then assign “A”.  If score < 93, then assign “Not A”.

22 Example 7  First class postage rates are given below.  Use a nested IF statement to help calculate postage! First-Class Mail (Retail Letters) - Postage Rates Weight not Over (Ounces)Single-Piece 1 $ $ $ $0.92

23 Example 7 (cont.)  The idea we need to implement in Excel is:  Weight ≤ 1 oz => $0.41  1 oz $0.58  2 oz $0.75  3 oz $0.92  Over 3.5 oz => cannot mail first class!  To do this we can use a nested IF command!  =IF(CELL#<=1,0.41,IF(CELL#<=2,0.58,IF(CELL#<= 3,0.75,IF(CELL#<=3.5,0.92,"cannot mail first class"))))

24 Example 7 (cont.)

25 The IF Function (cont.)  Up to 64 IF functions can be nested as value_if_true and value_if_false arguments to construct more elaborate tests.  When the value_if_true and value_if_false arguments are evaluated, IF returns the value returned by those statements.  If any of the arguments to IF are arrays, every element of the array is evaluated when the IF statement is carried out.  Microsoft Excel provides additional functions that are conditional, including COUNTIF, SUMIF, and others.  Another way to test many conditions is to use the LOOKUP, VLOOKUP, or HLOOKUP functions.

The LOOKUP Function  LOOKUP looks in a one-row or one-column range (known as a vector) for a value and returns a value from the same position in a second one-row or one-column range.  Syntax: LOOKUP(lookup_value,lookup_vector,result_vector)  lookup_value is a value that LOOKUP searches for in the first vector.  lookup_vector is a range that contains only one row or one column.  result_vector is a range that contains only one row or column. It must be the same size as lookup_vector. 26

The LOOKUP Function (cont.)  lookup_value can be a number, text, a logical value, or a name or reference that refers to a value.  The values in lookup_vector can be text, numbers, or logical values.  The values in lookup_vector must be placed in ascending order:...,-2, -1, 0, 1, 2,..., A-Z, FALSE, TRUE; otherwise, LOOKUP may not give the correct value.  Uppercase and lowercase text are equivalent.  If LOOKUP can't find the lookup_value, it matches the largest value in lookup_vector that is less than or equal to lookup_value.  If lookup_value is smaller than the smallest value in lookup_vector, LOOKUP gives the #N/A error value. 27

Example 8  The LOOKUP function can be used to calculate postage rates!  Try this command with the weights we used above in Example 7: 0.5, 1, 1.1, 2, 2.1, 3, 3.1, and 4 ounces.  =LOOKUP(weight,{0,1,2,3,3.5},{0.41, 0.58,0.75,0.92,"cannot mail first class"}) 28

Example 8 (cont.)  Does the postage get calculated correctly?  Notice that the postages for 1, 2, and 3 ounces are wrong.  How could we fix our LOOKUP function to get the correct postages?  One possibility – replace 1 with , 2 with , etc. in the look_up vector. 29

30 The IFERROR Function  Syntax: IFERROR(value,value_if_error)  value is the argument that is checked for an error.  value_if_error is the value to return if the formula evaluates to an error.  The following error types are evaluated: #N/A, #VALUE!, #REF!, #DIV/0!, #NUM!, #NAME?, or #NULL!.

The IFERROR Function (cont.)  If value or value_if_error is an empty cell, IFERROR treats it as an empty string value ("").  If value is an array formula, IFERROR returns an array of results for each cell in the range specified in value. 31

Example 9  Use the IFERROR function to create a “Division by Zero Checker”  What happens if any of the cells in columns A or B are blank? 32

Conditional Formatting  The formatting of a cell can be a determined by the cell contents!  In the Styles group of the Home tab, choose the Conditional Formatting drop-down menu.  The following examples are formatted conditionally, i.e. in terms of their contents, by choosing some of the built-in conditional formatting rules (large number available is new in Excel 2007)!  Highlight Cells Rules -> Less Than  Highlight Cells Rules -> Text that Contains  Data Bars  Top/Bottom Rules -> Above Average 33

Conditional Formatting (cont.)  Suppose we wish to use colors to highlight grades in a grade sheet, using colors to differentiate ranges of scores.  In particular, choose yellow, red, and green as the colors determined by scores in the range: score ≥ 92, 90 ≤ score < 92, score < 90, respectively!  One way to try to do this is via a built-in conditional formatting Color Scale, such as Green-Yellow-Red.  The drawback is that the built-in formatting may not match exactly what you want! 34

Conditional Formatting (cont.)  The other way is to create new conditional formatting rules!  To do this, choose Manage Rules from the Conditional Formatting Menu to pull up the Conditional Formatting Rules Manager.  Then choose New Rule, followed by Format Only Cells that Contain to set up the appropriate conditions. 35

36 References  Excel’s Help File and Microsoft’s Office Web pages: us/excel/HP aspx us/excel/HP aspx  About.com Excel IF Tutorial: celfunctions/a/if_funct_hub.htm celfunctions/a/if_funct_hub.htm  Microsoft Excel 2007 Bible by John Walkenbach