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Maths & Trig, Statistical functions Slide 2 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. Slide 3 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) Slide 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 ) Slide 5 EVEN Returns number rounded up to the nearest even integer You can use this function for processing items that come in twos Slide 6 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. Slide 7 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) Slide 8 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. Slide 9 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) Slide 10 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. Slide 11 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) Slide 12 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. Slide 13 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 Slide 14 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 Slide 15 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 0.234 up to the nearest multiple of 0.01 (0.24) Example: Slide 16 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. Slide 17 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. Slide 18 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 0.234 down to the nearest multiple of 0.01 (0.23) Slide 19 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 Slide 20 Conti Example: =ROUND(2.15, 1)Rounds 2.15 to one decimal place (2.2) =ROUND(2.149, 1)Rounds 2.149 to one decimal place (2.1) =ROUND(-1.475, 2)Rounds -1.475 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) Slide 21 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. Slide 22 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. Slide 23 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) Slide 24 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. Slide 25 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) Slide 26 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) Slide 27 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. Slide 28 Conti FormulaResult =COMBIN(8,2)Possible two-person teams that can be formed from 8 candidates (28) Slide 29 EXP Returns e raised to the power of number. The constant e equals 2.71828182845904, the base of the natural logarithm Syntax EXP(number) Number is the exponent applied to the base e. Slide 30 Conti Remarks To calculate powers of other bases, use the exponentiation operator (^) EXP is the inverse of LN, the natural logarithm of number Slide 31 Conti FormulaResult =EXP(1)Approximate value of e (2.718282) =EXP(2)Base of the natural logarithm e raised to the power of 2 (7.389056) Slide 32 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. Slide 33 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) Slide 34 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. Slide 35 Conti FormulaDescription (Result) =INT(8.9)Rounds 8.9 down (8) =INT(-8.9)Rounds -8.9 down (-9) Slide 36 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 Slide 37 Conti Example: FormulaDescription (Result) =LOG(10)Logarithm of 10 (1) =LOG(8, 2)Logarithm of 8 with base 2 (3) =LOG(86, 2.7182818)Logarithm of 86 with base e (4.454347) Slide 38 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. Slide 39 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) Slide 40 PI Returns the value of Pi accurate to 15 digits This function takes no arguments It returns 3.141592654 value of Pi Slide 41 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 Slide 42 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. Slide 43 Conti Example A Data 15 215 330 FormulaDescription (Result) =PRODUCT(A1:A3)Multiplies the numbers above (2250) =PRODUCT(A1:A3, 2)Multiplies the numbers above and 2 (4500) Slide 44 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 Slide 45 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) Slide 46 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. Slide 47 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(3.14159, 3)Rounds 3.14159 up to three decimal places (3.142) =ROUNDUP(-3.14159, 1)Rounds -3.14159 up to one decimal place (-3.2) Slide 48 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. Slide 49 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(3.14159, 3)Rounds 3.14159 down to three decimal places (3.141) =ROUNDDOWN(-3.14159, 1)Rounds -3.14159 down to one decimal place (-3.1) Slide 50 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. Slide 51 Conti Example: =SIGN(10)Sign of a positive number (1) =SIGN(4-4)Sign of zero (0) =SIGN(-0.00001)Sign of a negative number (-1) Slide 52 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 Slide 53 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. Slide 54 Conti Function_num (includes hidden values) Function_num (ignores hidden values) Function 1101AVERAGE 2102COUNT 3103COUNTA 4104MAX 5105MIN 6106PRODUCT 7107STDEV 8108STDEVP 9109SUM 10110VAR 11111VARP Slide 55 Conti Example: A Data 1120 210 3150 423 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) Slide 56 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. Slide 57 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 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 Slide 58160000",B2:B5)Sum of the commissions for"> 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)"> 160000",B2:B5)Sum of the commissions for" title="Conti AB 1Property ValueCommission 2100,0007,000 3200,00014,000 4300,00021,000 5400,00028,000 =SUMIF(A2:A5,">160000",B2:B5)Sum of the commissions for"> Conti AB 1Property ValueCommission 2100,0007,000 3200,00014,000 4300,00021,000 5400,00028,000 =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) Slide 59 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). Slide 60 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)