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Statistical Functions AVERAGE AVERAGEIF AVERAGEIFS COUNT COUNTA COUNTIF COUNTIFS MAX MIN LARGE SMALL Logical Functions AND OR NOT IF NESTED IF Mathematical Functions SUM SUMIF SUMIFS ROUND

=ROUND(number,num_digits) SUM =SUM(number1,[number2],...) SUMIF =SUMIF(range,criteria,[sum_range]) SUMIFS =SUMIFS(sum_range, criteria_range1, criteria1, [criteria_range2, criteria2],...)

Microsoft ® Excel ® Mathematical Functions Syntax: =ROUND(number, num_digits) Arguments: number Required  The number that you want to round. num_digits Required  The number of digits to which you want to round the number argument.

Microsoft ® Excel ® Mathematical Functions Description: Rounds a number to a specified number of digits. Remarks: If num_digits is greater than 0 (zero), then number is rounded to the specified number of decimal places. If num_digits is 0, the number is rounded to the nearest integer. If num_digits is less than 0, the number is rounded to the left of the decimal point. Errors: None

Microsoft ® Excel ® Mathematical Functions =ROUND(-1.475,2) Rounds to two decimal places

Microsoft ® Excel ® Mathematical Functions Syntax: =SUM(number1, [number2], [number3], [number4],...) Arguments: number1 Required  The first item that you want to add. number2, number3, number4,... Optional  The remaining items that you want to add, up to a total of 255 items.

Microsoft ® Excel ® Mathematical Functions Description: Adds all the numbers that you specify as arguments. Remarks: Each argument can be a range, a cell reference, an array, a constant, a formula, or the result from another function. If an argument is an array or reference, only numbers in that array or reference are counted. Empty cells, logical values, or text in the array or reference are ignored. Errors: If any arguments are error values, or if any arguments are text that cannot be translated into numbers, Excel displays an error.

Microsoft ® Excel ® Mathematical Functions

Syntax: =SUMIF(range, criteria, [sum_range]) Arguments: range Required  The range of cells that you want evaluated by criteria. o Cells in each range must be numbers or names, arrays, or references that contain numbers. o Blank and text values are ignored.  criteria Required  The criteria in the form of a number, expression, a cell reference, text, or a function that defines which cells will be added. o Criteria can be expressed as 32, ">32", B5, "32", "apples", or TODAY(). sum_range Optional  The actual cells to add, if you want to add cells other than those specified in the range argument. o Excel adds the cells that are specified in the range argument (the same cells to which the criteria is applied).

Microsoft ® Excel ® Mathematical Functions Description: Sums the values in a range that meet criteria that you specify. Remarks: See the Microsoft ® Excel ® help for additional remarks. Errors: None

Microsoft ® Excel ® Mathematical Functions

 Syntax =SUMIFS(sum_range, criteria_range1, criteria1, [criteria_range2, criteria2],...) Arguments  sum_range Required. One or more cells to sum, including numbers or names, ranges, or cell references. Blank and text values are ignored.  criteria_range1 Required. The first range in which to evaluate the associated criteria.  criteria1 Required. The criteria in the form of a number, expression, cell reference, or text that define which cells in the criteria_range1 argument will be added. For example, criteria can be expressed as 32, ">32", B4, "apples", or "32.“  criteria_range2, criteria2, … Optional. Additional ranges and their associated criteria. Up to 127 range/criteria pairs are allowed.

 Remarks  Each cell in the sum_range argument is summed only if all of the corresponding criteria specified are true for that cell. For example, suppose that a formula contains two criteria_range arguments. If the first cell of criteria_range1 meets criteria1, and the first cell of criteria_range2 meets critera2, the first cell of sum_range is added to the sum, and so on, for the remaining cells in the specified ranges.  Cells in the sum_range argument that contain TRUE evaluate to 1; cells in sum_range that contain FALSE evaluate to 0 (zero).  Unlike the range and criteria arguments in the SUMIF function, in the SUMIFS function, each criteria_range argument must contain the same number of rows and columns as the sum_range argument.  You can use the wildcard characters — the question mark (?) and asterisk (*) — in criteria. A question mark matches any single character; an asterisk matches any sequence of characters. If you want to find an actual question mark or asterisk, type a tilde (~) before the character.

Quantity Sold Product Salespers on 5Apples Artichokes Bananas 1 12Bananas 2 10Carrots 1 33Carrots 2 FormulaDescription Result =SUMIFS(A2:A9, B2:B9, "=A*", C2:C9, 1) Adds the total number of products sold that begin with "A" and that were sold by Salesperson =SUMIFS(A2:A9, B2:B9, "<>Bananas", C2:C9, 1) Adds the total number of products (not including Bananas) sold by Salesperson 1. 30

AVERAGE=AVERAGE(number1, [number2],...) AVERAGEIF=AVERAGEIF(range,criteria,[average_range]) AVERAGEIFS =AVERAGEIFS(average_range,criteria_range1,criteria1,criteria_range2,criteria2…) COUNT=COUNT(value1, [value2],...) COUNTIF=COUNTIF(range, criteria) COUNTIFS=COUNTIFS(criteria_range1, criteria1, [criteria_range2, criteria2]…) MAX=MAX(number1,[number2],...) MIN=MIN(number1,[number2],...) LARGE=LARGE(array,k) SMALL=SMALL(array,k)

Microsoft ® Excel ® Statistical Functions Syntax: =AVERAGE(number1, [number2],...) Arguments: number1 Required  The first number, cell reference, or range for which you want the average. number2,... Optional  Additional numbers, cell references or ranges for which you want the average, up to a maximum of 255.

Microsoft ® Excel ® Statistical Functions Description: Returns the average (arithmetic mean) of the arguments. Remarks: Arguments can either be numbers or names, ranges, or cell references that contain numbers. Logical values and text representations of numbers that you type directly into the list of arguments are counted. If a range or cell reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included. Errors: Arguments that are error values or text that cannot be translated into numbers cause errors.

Microsoft ® Excel ® Statistical Functions

Syntax: =AVERAGEIF(range, criteria, [average_range]) Arguments: range Required  One or more cells to average, including numbers or names, arrays, or references that contain numbers. criteria Required  The criteria in the form of a number, expression, cell reference, or text that defines which cells are averaged. average_range Optional  The actual set of cells to average.

Microsoft ® Excel ® Statistical Functions Description: Returns the average (arithmetic mean) of all the cells in a range that meet a given criteria. Remarks: If average_range is omitted, range is used. Cells in range that contain TRUE or FALSE are ignored. If a cell in average_range is an empty cell, AVERAGEIF ignores it. If a cell in criteria is empty, AVERAGEIF treats it as a 0 value. Errors: #DIV/0 – If range is a blank or text value. #DIV/0 – If no cells in the range meet the criteria.

Microsoft ® Excel ® Statistical Functions =AVERAGEIF(B2:B5,"<23000")

Microsoft ® Excel ® Statistical Functions =AVERAGEIF(B2:B5,"<23000") =14000

Microsoft ® Excel ® Statistical Functions =AVERAGEIF(A2:A5,"<95000")

Microsoft ® Excel ® Statistical Functions =AVERAGEIF(A2:A5,"<95000") =#DIV/0

Microsoft ® Excel ® Statistical Functions =AVERAGEIF(A2:A5,">250000",B2:B5)

Microsoft ® Excel ® Statistical Functions =AVERAGEIF(A2:A5,">250000",B2:B5) =24500

 Syntax =AVERAGEIFS(average_range,criteria_range1,crite ria1,criteria_range2,criteria2…) Argument  Average_range is one or more cells to average, including numbers or names, arrays, or references that contain numbers.  Criteria_range1, criteria_range2, … are 1 to 127 ranges in which to evaluate the associated criteria.  Criteria1, criteria2, … are 1 to 127 criteria in the form of a number, expression, cell reference, or text that define which cells will be averaged. For example, criteria can be expressed as 32, "32", ">32", "apples", or B4.

 Remarks  If average_range is a blank or text value, AVERAGEIFS returns the #DIV0! error value.  If a cell in a criteria range is empty, AVERAGEIFS treats it as a 0 value.  Cells in range that contain TRUE evaluate as 1; cells in range that contain FALSE evaluate as 0 (zero).  Each cell in average_range is used in the average calculation only if all of the corresponding criteria specified are true for that cell.  Unlike the range and criteria arguments in the AVERAGEIF function, in AVERAGEIFS each criteria_range must be the same size and shape as sum_range.  If cells in average_range cannot be translated into numbers, AVERAGEIFS returns the #DIV0! error value.  If there are no cells that meet all the criteria, AVERAGEIFS returns the #DIV/0! error value.  You can use the wildcard characters, question mark (?) and asterisk (*), in criteria. A question mark matches any single character; an asterisk matches any sequence of characters. If you want to find an actual question mark or asterisk, type a tilde (~) before the character.

Microsoft ® Excel ® Statistical Functions Syntax: =COUNT(value1, [value2],...) Arguments: value1 Required  The first item, cell reference, or range within which you want to count numbers. value2,... Optional  Up to 255 additional items, cell references, or ranges within which you want to count numbers.

Microsoft ® Excel ® Statistical Functions Description: Counts the number of cells that contain numbers, and counts numbers within the list of arguments. Remarks: Arguments that are numbers, dates, or a text representation of numbers (for example, a number enclosed in quotation marks, such as "1") are counted. Logical values and text representations of numbers that you type directly into the list of arguments are counted. Arguments that are error values or text that cannot be translated into numbers are not counted. If an argument is an array or reference, only numbers in that array or reference are counted. Empty cells, logical values, text, or error values in the array or reference are not counted. Errors: None

Microsoft ® Excel ® Statistical Functions

Syntax: =COUNTA(value1, [value2],...) Arguments: value1 Required  The first argument representing the values that you want to count. value2,... Optional  Additional arguments representing the values that you want to count, up to a maximum of 255 arguments.

Microsoft ® Excel ® Statistical Functions Description: Counts the number of cells that are not empty in a range. Remarks: Counts cells containing any type of information, including error values and empty text ("“). The COUNTA function does not count empty cells. Errors: None

Microsoft ® Excel ® Statistical Functions =COUNTA(A1:A8) = 7

Microsoft ® Excel ® Statistical Functions Syntax: =COUNTIF(range, criteria) Arguments: range Required  One or more cells to count, including numbers or names, arrays, or references that contain numbers. o Blank and text values are ignored.  criteria Required  A number, expression, cell reference, or text string that defines which cells will be counted. o Criteria can be expressed as 32, ">32", B4, "apples", or "32".

Microsoft ® Excel ® Statistical Functions Description: Counts the number of cells within a range that meet a single criterion that you specify. Remarks: See the Microsoft ® Excel ® help for additional remarks. Criteria are case insensitive Errors: None

Microsoft ® Excel ® Statistical Functions

 Syntax =COUNTIFS(criteria_range1, criteria1, [criteria_range2, criteria2]…) Arguments:  criteria_range1 Required. The first range in which to evaluate the associated criteria.  criteria1 Required. The criteria in the form of a number, expression, cell reference, or text that define which cells will be counted. For example, criteria can be expressed as 32, ">32", B4, "apples", or "32".  criteria_range2, criteria2,... Optional. Additional ranges and their associated criteria. Up to 127 range/criteria pairs are allowed.  Important Each additional range must have the same number of rows and columns as the criteria_range1 argument. The ranges do not have to be adjacent to each other.

 Remarks  Each range's criteria is applied one cell at a time. If all of the first cells meet their associated criteria, the count increases by 1. If all of the second cells meet their associated criteria, the count increases by 1 again, and so on until all of the cells are evaluated.  If the criteria argument is a reference to an empty cell, the COUNTIFS function treats the empty cell as a 0 value.  You can use the wildcard characters— the question mark (?) and asterisk (*) — in criteria. A question mark matches any single character, and an asterisk matches any sequence of characters. If you want to find an actual question mark or asterisk, type a tilde (~) before the character.

Microsoft ® Excel ® Statistical Functions Syntax: =LARGE(array,k) Arguments: array Required  The array or range of data for which you want to determine the k- th largest value.  k Required  The position (from the largest) in the array or cell range of data to return.

Microsoft ® Excel ® Statistical Functions Description: Returns the k-th largest value in a data set. Remarks: If n is the number of data points in a range, then LARGE(array,1) returns the largest value. If n is the number of data points in a range, then LARGE(array,n) returns the smallest value. Errors: #NUM! – If array is empty #NUM! – If k ≤ 0 #NUM! – If k is greater than the number of data points

=LARGE(array,k) 3rd largest number in the numbers in columns A and B

=LARGE(array,k) =LARGE(A2:B6 3rd largest number in the numbers in columns A and B

=LARGE(array,k) =LARGE(A2:B6,3) 3rd largest number in the numbers in columns A and B

=LARGE(array,k) =LARGE(A2:B6,3) 3rd largest number in the numbers in columns A and B List the numbers in descending order: =5

=LARGE(array,k) 7th largest number in the numbers in columns A and B

=LARGE(array,k) =LARGE(A2:B6 7th largest number in the numbers in columns A and B

=LARGE(array,k) =LARGE(A2:B6,7) 7th largest number in the numbers in columns A and B

=LARGE(array,k) =LARGE(A2:B6,7) 7th largest number in the numbers in columns A and B List the numbers in descending order:

=LARGE(array,k) =LARGE(A2:B6,7) 7th largest number in the numbers in columns A and B List the numbers in descending order: =4

Microsoft ® Excel ® Statistical Functions Syntax: =SMALL(array,k) Arguments: array Required  The array or range of data for which you want to determine the k- th smallest value.  k Required  The position (from the smallest) in the array or cell range of data to return.

Microsoft ® Excel ® Statistical Functions Description: Returns the k-th smallest value in a data set. Remarks: If n is the number of data points in a range, then SMALL(array,1) returns the smallest value. If n is the number of data points in a range, then SMALL(array,n) returns the largest value. Errors: #NUM! – If array is empty #NUM! – If k ≤ 0 #NUM! – If k is greater than the number of data points

=SMALL(array,k) 4th smallest number in first column

=SMALL(array,k) =SMALL(A2:A10 4th smallest number in first column

=SMALL(array,k) =SMALL(A2:A10,4) 4th smallest number in first column List the numbers in ascending order:

=SMALL(array,k) =SMALL(A2:A10,4) 4th smallest number in first column List the numbers in ascending order: =4

=SMALL(array,k) 2nd smallest number in second column

=SMALL(array,k) =SMALL(B2:B10 2nd smallest number in second column

=SMALL(array,k) =SMALL(B2:B10,2) 2nd smallest number in second column List the numbers in ascending order:

=SMALL(array,k) =SMALL(B2:B10,2) 2nd smallest number in second column =3 List the numbers in ascending order:

AND =AND(logical1, [logical2],...) OR =OR(logical1, [logical2],...) NOT =NOT(logical) IF =IF(logical_test, [value_if_true], [value_if_false])

Microsoft ® Excel ® Logical Functions Syntax: =AND(logical1, [logical2],...) Arguments: logical1 Required  The first condition that you want to test that can evaluate to either TRUE or FALSE. logical2,... Optional  Additional conditions that you want to test that can evaluate to either TRUE or FALSE, up to a maximum of 255 conditions.

Microsoft ® Excel ® Logical Functions Description: Returns FALSE if one or more arguments is FALSE Otherwise, all arguments must evaluate TRUE Remarks: Arguments must evaluate to logical values Arguments must be arrays or references that contain logical values Text and empty cells are ignored in arrays or references Errors: #VALUE – If no logical values exist in a specified range

Microsoft ® Excel ® Logical Functions 

Microsoft ® Excel ® Logical Functions 

Microsoft ® Excel ® Logical Functions Syntax: =OR(logical1, [logical2],...) Arguments: logical1 Required  The first condition that you want to test that can evaluate to either TRUE or FALSE. logical2,... Optional  Additional conditions that you want to test that can evaluate to either TRUE or FALSE, up to a maximum of 255 conditions.

Microsoft ® Excel ® Logical Functions Description: Returns TRUE if one or more arguments is TRUE Otherwise, all arguments must evaluate FALSE Remarks: Arguments must evaluate to logical values Arguments must be arrays or references that contain logical values Text and empty cells are ignored in arrays or references Errors: #VALUE – If no logical values exist in a specified range

Microsoft ® Excel ® Logical Functions  

Microsoft ® Excel ® Logical Functions Syntax: =NOT(logical) Arguments: logical Required  A value or expression that can be evaluated to TRUE or FALSE.

Microsoft ® Excel ® Logical Functions Description: Reverses the value of its argument. Remarks: If logical is FALSE, NOT returns TRUE if logical is TRUE, NOT returns FALSE Errors: None

Microsoft ® Excel ® Logical Functions

Syntax: =IF(logical_test, [value_if_true], [value_if_false]) Arguments: logical_test Required  Any value or expression that can be evaluated to TRUE or FALSE. value_if_true Required The value that you want to be returned if the logical_test argument evaluates to TRUE. If logical_test evaluates to TRUE and the value_if_true argument is omitted (that is, there is only a comma following the logical_test argument), the IF function returns 0 (zero). To display the word TRUE, use the logical value TRUE for the value_if_true argument.

Microsoft ® Excel ® Logical Functions Syntax: =IF(logical_test, [value_if_true], [value_if_false]) Arguments: value_if_false Optional  The value that you want to be returned if the logical_test argument evaluates to FALSE.  If logical_test evaluates to FALSE and the value_if_false argument is omitted, (that is, there is no comma following the value_if_true argument), the IF function returns the logical value FALSE.  If logical_test evaluates to FALSE and the value of the value_if_false argument is omitted (that is, in the IF function, there is a comma following the value_if_true argument), the IF function returns the value 0 (zero).

Microsoft ® Excel ® Logical Functions Description: The IF function returns one value if a condition you specify evaluates to TRUE, and another value if that condition evaluates to FALSE. Remarks: Up to 7 IF functions can be nested as value_if_true and value_if_false arguments to construct more elaborate tests. (2003) Up to 64 IF functions can be nested as value_if_true and value_if_false arguments to construct more elaborate tests. (2007) If any of the arguments to IF are arrays, every element of the array is evaluated when the IF statement is carried out. Errors: None

Microsoft ® Excel ® Logical Functions value_if_true  [value_if_false ]

 m m  A nested IF statement says something like...  "If the answer is yes, do this. If the answer is no do this or this (depending on...“  Syntax: IF( condition1, value_if_true, IF( condition2, value_if_true, value_if_false )) Microsoft ® Excel ® Date Functions

 What was the percentage grade you got on your last test? ◦ You received 75% (Cell Address is A1) ◦ If less than 60%- Sorry, you failed; Less than 70%- You got a D; Less than 80%- You got a C; Less than 90% - You got a B; 90% or more – You got an A

 =IF(A1<60,"Sorry you failed",IF(A1<70,"You got a D",IF(A1<80,"You got a C",IF(A1<90,"You got a B","You got an A"))))