Maths & Trig, Statistical functions

ABS Returns the absolute value of a number The absolute value of a number is the number without its sign Syntax ◦ ABS(number)  Where, Number is the real number of which you want the absolute value.

Conti… Example: FormulaDescription (Result) ABS(2)Absolute value of 2 (2) ABS(-2)Absolute value of -2 (2) ABS(A2) Absolute value of -4 (4)

SUM The SUM function provides a quick way to sum columns or rows of numbers in an Excel worksheet Syntax: ◦ SUM ( Number1, Number2,... Number255 )

EVEN Returns number rounded up to the nearest even integer You can use this function for processing items that come in twos

Conti… Syntax ◦ EVEN(number)  Number is the value to round Remarks ◦ If number is nonnumeric, EVEN returns the #VALUE! error value ◦ If number is an even integer, no rounding occurs.

Conti… Example: =EVEN(1.5)Rounds 1.5 up to the nearest even integer (2) =EVEN(3)Rounds 3 up to the nearest even integer (4) =EVEN(2)Rounds 2 up to the nearest even integer (2) =EVEN(-1)Rounds -1 up to the nearest even integer (-2)

MOD Returns the remainder after number is divided by divisor. The result has the same sign as divisor Syntax ◦ MOD(number,divisor)  Number is the number for which you want to find the remainder.  Divisor is the number by which you want to divide number.

Conti… Remarks ◦ If divisor is 0, MOD returns the #DIV/0! error value Example: =MOD(3, 2)Remainder of 3/2 (1) =MOD(-3, 2)Remainder of -3/2. The sign is the same as divisor (1) =MOD(3, -2)Remainder of 3/-2. The sign is the same as divisor (-1) =MOD(-3, -2)Remainder of -3/-2. The sign is the same as divisor (-1)

SQRT Returns a positive square root. Syntax ◦ SQRT(number)  Number is the number for which you want the square root. Remark ◦ If number is negative, SQRT returns the #NUM! error value.

Conti… Example: =SQRT(16)Square root of 16 (4) =SQRT(A2)Square root of the number above. Because the number is negative, an error is returned (#NUM!) =SQRT(ABS(A2))Square root of the absolute value of the number above (4)

CEILING Returns number rounded up, away from zero, to the nearest multiple of significance For example, if you want to avoid using pennies in your prices and your product is priced at $4.42, use the formula =CEILING(4.42,0.05) to round prices up to the nearest nickel.

Conti… Syntax: ◦ CEILING(number, significance)  Number is the value you want to round  Significance is the multiple to which you want to round Remarks ◦ If either argument is nonnumeric, CEILING returns the #VALUE! error value

Conti… ◦ Regardless of the sign of number, a value is rounded up when adjusted away from zero. If number is an exact multiple of significance, no rounding occurs ◦ If number and significance have different signs, CEILING returns the #NUM! error value

Conti… =CEILING(2.5, 1)Rounds 2.5 up to nearest multiple of 1 (3) =CEILING(-2.5, -2)Rounds -2.5 up to nearest multiple of -2 (-4) =CEILING(-2.5, 2)Returns an error, because -2.5 and 2 have different signs (#NUM!) =CEILING(1.5, 0.1)Rounds 1.5 up to the nearest multiple of 0.1 (1.5) =CEILING(0.234, 0.01)Rounds up to the nearest multiple of 0.01 (0.24) Example:

FLOOR Rounds number down, toward zero, to the nearest multiple of significance Syntax ◦ FLOOR(number, significance)  Number is the numeric value you want to round.  Significance is the multiple to which you want to round. Remarks ◦ If either argument is nonnumeric, FLOOR returns the #VALUE! error value.

Conti… ◦ If number and significance have different signs, FLOOR returns the #NUM! error value. ◦ Regardless of the sign of number, a value is rounded down when adjusted away from zero. If number is an exact multiple of significance, no rounding occurs.

Conti… Example: =FLOOR(2.5, 1)Rounds 2.5 down to nearest multiple of 1 (2) =FLOOR(-2.5, -2)Rounds -2.5 down to nearest multiple of -2 (-2) =FLOOR(-2.5, 2)Returns an error, because -2.5 and 2 have different signs (#NUM!) =FLOOR(1.5, 0.1)Rounds 1.5 down to the nearest multiple of 0.1 (1.5) =FLOOR(0.234, 0.01)Rounds down to the nearest multiple of 0.01 (0.23)

ROUND Rounds a number to a specified number of digits. Syntax ◦ ROUND(number,num_digits)  Number is the number you want to round  Num_digits specifies the number of digits to which you want to round number 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, then number is rounded to the nearest integer ◦ If num_digits is less than 0, then number is rounded to the left of the decimal point

Conti… Example: =ROUND(2.15, 1)Rounds 2.15 to one decimal place (2.2) =ROUND(2.149, 1)Rounds to one decimal place (2.1) =ROUND(-1.475, 2)Rounds to two decimal places (-1.48) =ROUND(21.5, -1)Rounds 21.5 to one decimal place to the left of the decimal point (20)

GCD Returns the greatest common divisor of two or more integers The greatest common divisor is the largest integer that divides both number1 and number2 without a remainder Syntax ◦ GCD(number1,number2,...)  Number1, number2,... are 1 to 255 values. If any value is not an integer, it is truncated.

Conti… Remarks ◦ If any argument is nonnumeric, GCD returns the #VALUE! error value. ◦ If any argument is less than zero, GCD returns the #NUM! error value. ◦ One divides any value evenly. ◦ A prime number has only itself and one as even divisors.

Conti… Example: =GCD(5, 2)Greatest common divisor of 5 and 2 (1) =GCD(24, 36)Greatest common divisor of 24 and 36 (12) =GCD(7, 1)Greatest common divisor of 7 and 1 (1) =GCD(5, 0)Greatest common divisor of 5 and 0 (5)

LCM Returns the least common multiple of integers The least common multiple is the smallest positive integer that is a multiple of all integer arguments number1, number2, and so on. Use LCM to add fractions with different denominators. Syntax ◦ LCM(number1,number2,...)  Number1, number2,... are 1 to 255 values for which you want the least common multiple. If value is not an integer, it is truncated.

Conti… Remarks ◦ If any argument is nonnumeric, LCM returns the #VALUE! error value. ◦ If any argument is less than zero, LCM returns the #NUM! error value. Example: =LCM(5, 2)Least common multiple of 5 and 2 (10) =LCM(24, 36)Least common multiple of 24 and 36 (72)

COMBIN Returns the number of combinations for a given number of items Use COMBIN to determine the total possible number of groups for a given number of items Syntax ◦ COMBIN(number,number_chosen)

Conti… ◦ Number is the number of items. ◦ Number_chosen is the number of items in each combination. Remarks ◦ Numeric arguments are truncated to integers. ◦ If either argument is nonnumeric, COMBIN returns the #VALUE! error value. ◦ If number < 0, number_chosen < 0, or number < number_chosen, COMBIN returns the #NUM! error value.

Conti… FormulaResult =COMBIN(8,2)Possible two-person teams that can be formed from 8 candidates (28)

EXP Returns e raised to the power of number. The constant e equals , the base of the natural logarithm Syntax ◦ EXP(number)  Number is the exponent applied to the base e.

Conti… Remarks ◦ To calculate powers of other bases, use the exponentiation operator (^) ◦ EXP is the inverse of LN, the natural logarithm of number

Conti… FormulaResult =EXP(1)Approximate value of e ( ) =EXP(2)Base of the natural logarithm e raised to the power of 2 ( )

FACT Returns the factorial of a number. The factorial of a number is equal to 1*2*3*...* number Syntax ◦ FACT(number)  Number is the nonnegative number for which you want the factorial. If number is not an integer, it is truncated.

Conti… FormulaDescription (Result) =FACT(5)Factorial of 5, or 1*2*3*4*5 (120) =FACT(1.9)Factorial of the integer of 1.9 (1) =FACT(0)Factorial of 0 (1) =FACT(-1)Negative numbers cause an error value (#NUM!) =FACT(1)Factorial of 1 (1)

INT Rounds a number down to the nearest integer Syntax ◦ INT(number)  Number is the real number you want to round down to an integer.

Conti… FormulaDescription (Result) =INT(8.9)Rounds 8.9 down (8) =INT(-8.9)Rounds -8.9 down (-9)

LOG Returns the logarithm of a number to the base you specify. Syntax ◦ LOG(number, base)  Number is the positive real number for which you want the logarithm  Base is the base of the logarithm. If base is omitted, it is assumed to be 10

Conti… Example: FormulaDescription (Result) =LOG(10)Logarithm of 10 (1) =LOG(8, 2)Logarithm of 8 with base 2 (3) =LOG(86, )Logarithm of 86 with base e ( )

MROUND Returns a number rounded to the desired multiple Syntax ◦ MROUND(number,multiple)  Number is the value to round.  Multiple is the multiple to which you want to round number.

Conti… Remark ◦ MROUND rounds up, away from zero, if the remainder of dividing number by multiple is greater than or equal to half the value of multiple Example FormulaDescription (Result) =MROUND(10, 3)Rounds 10 to a nearest multiple of 3 (9) =MROUND(-10, -3)Rounds -10 to a nearest multiple of -3 (-9)

PI Returns the value of Pi accurate to 15 digits This function takes no arguments It returns value of Pi

POWER Returns the result of a number raised to power Syntax ◦ POWER(Number, Power)  Where, Number is base number, any real number Example POWER(4,2) returns 16 POWER(10,2) returns 100

PRODUCT Multiplies all the numbers given as arguments and returns the product. Syntax ◦ PRODUCT(number1,number2,...)  Number1, number2,... are 1 to 255 numbers that you want to multiply.

Conti… Example A Data FormulaDescription (Result) =PRODUCT(A1:A3)Multiplies the numbers above (2250) =PRODUCT(A1:A3, 2)Multiplies the numbers above and 2 (4500)

QUOTIENT Returns the integer portion of a division Use this function when you want to discard the remainder of a division Syntax ◦ QUOTIENT(numerator, denominator)  Numerator is the dividend  Denominator is the divisor

Conti… Example FormulaDescription (Result) =QUOTIENT(5, 2)Integer portion of 5/2 (2) =QUOTIENT(4.5, 3.1)Integer portion of 4.5/3.1 (1) =QUOTIENT(-10, 3)Integer portion of -10/3 (-3)

ROUNDUP Rounds a number up, away from 0 (zero) Syntax ◦ ROUNDUP(number,num_digits)  Number is any real number that you want rounded up.  Num_digits is the number of digits to which you want to round number.

Conti… Example =ROUNDUP(3.2,0)Rounds 3.2 up to zero decimal places (4) =ROUNDUP(76.9,0)Rounds 76.9 up to zero decimal places (77) =ROUNDUP( , 3)Rounds up to three decimal places (3.142) =ROUNDUP( , 1)Rounds up to one decimal place (-3.2)

ROUNDDOWN Rounds a number down, toward zero. Syntax ◦ ROUNDDOWN(number,num_digits)  Number is any real number that you want rounded down.  Num_digits is the number of digits to which you want to round number.

Conti… Example: =ROUNDDOWN(3.2, 0)Rounds 3.2 down to zero decimal places (3) =ROUNDDOWN(76.9,0)Rounds 76.9 down to zero decimal places (76) =ROUNDDOWN( , 3)Rounds down to three decimal places (3.141) =ROUNDDOWN( , 1)Rounds down to one decimal place (-3.1)

SIGN Determines the sign of a number Returns 1 if the number is positive, zero (0) if the number is 0, and -1 if the number is negative Syntax ◦ SIGN(number)  Number is any real number.

Conti… Example: =SIGN(10)Sign of a positive number (1) =SIGN(4-4)Sign of zero (0) =SIGN( )Sign of a negative number (-1)

SUBTOTAL Returns a subtotal in a list or database It is generally easier to create a list with subtotals by using the Subtotal command in the Outline group on the Data tab

Conti… Syntax ◦ SUBTOTAL(function_num, ref1, ref2,...)  Function_num is the number 1 to 11 (includes hidden values) or 101 to 111 (ignores hidden values) that specifies which function to use in calculating subtotals within a list.

Conti… Function_num (includes hidden values) Function_num (ignores hidden values) Function 1101AVERAGE 2102COUNT 3103COUNTA 4104MAX 5105MIN 6106PRODUCT 7107STDEV 8108STDEVP 9109SUM 10110VAR 11111VARP

Conti… Example: A Data FormulaDescription (Result) =SUBTOTAL(9,A2:A5)Subtotal of the column above using the SUM function (303) =SUBTOTAL(1,A2:A5)Subtotal of the column above using the AVERAGE function (75.75)

SUMIF Adds the cells specified by a given criteria Syntax ◦ SUMIF(range,criteria,sum_range)  Range is the range of cells that you want evaluated by criteria. Cells in each range must be numbers or names, arrays, or references that contain numbers. Blank and text values are ignored.

Conti…  Criteria is the criteria in the form of a number, expression, or text that defines which cells will be added. For example, criteria can be expressed as 32, "32", ">32", or "apples".  Sum_range are the actual cells to add if their corresponding cells in range match criteria. If sum_range is omitted, the cells in range are both evaluated by criteria and added if they match criteria

Conti… AB 1Property ValueCommission 2100,0007, ,00014, ,00021, ,00028,000 =SUMIF(A2:A5,">160000",B2:B5)Sum of the commissions for property values over 160,000 (63,000) =SUMIF(A2:A5,">160000")Sum of the property values over 160,000 (900,000) =SUMIF(A2:A5,"=300000",B2:B3)Sum of the commissions for property values equal to 300,000 (21,000)

TRUNC Truncates a number to an integer by removing the fractional part of the number Syntax ◦ TRUNC(number,num_digits)  Number is the number you want to truncate.  Num_digits is a number specifying the precision of the truncation. The default value for num_digits is 0 (zero).

Conti… Example: FormulaDescription (Result) =TRUNC(8.9)Integer part of 8.9 (8) =TRUNC(-8.9)Integer part of -8.9 (-8) =TRUNC(PI())Integer part of pi (3)