Calculating & Reporting Healthcare Statistics Second Edition Chapter 2 Mathematics Review

Mathematics Review Fractions A fraction is one or more parts of the whole The top number is called the numerator The bottom number is called the denominator ©2006 All rights reserved.

Mathematics Review The quotient It is the number you get when you divide the numerator by the denominator This number may be expressed in decimals ©2006 All rights reserved.

Mathematics Review Decimal Fractions Simply referred to as decimals In the decimal number 14.37, the digits 3 and 7 are called decimal digits All digits to the right of the decimal point are called decimal digits The decimal point is merely a way of separating the whole number part (14) from the fraction part (.37) 14.37 simply means there are 14 whole parts in this value plus .37 parts. The decimal .5 is usually written as 0.5 in order to call attention to the decimal point ©2006 All rights reserved.

Mathematics Review Rounding Whole Numbers Rounding to the Nearest Ten A process of approximating a number One way of approximating is to round the number to the nearest 10, 100, and so on Rounding to the Nearest Ten For example the number 31 is between 30 and 40, but it is closer to 30 37 is between 30 and 40, but it is closer to 40 So when you are asked to round to the nearest ten, 31 is rounded to 30 and 37 is rounded to 40 If a number is exactly between the two multiples of ten, then the rule of thumb is to round up 35 would be rounded up to 40 Anything between 35 and 39 would be rounded to 40 Anything between 34 and 31 would be rounded down to 30 ©2006 All rights reserved.

Mathematics Review Rounding to the Nearest Hundred 327 is between 300 and 400 The 2 in the tens place, indicates we should round down to 300 7878 is between 7800 and 7900 The second 7 (in the tens place) indicates that we should round up so 7878 is near to 7900 ©2006 All rights reserved.

Mathematics Review Rounding Decimals Each healthcare facility has its own policy on the number of decimal places used in computing and reporting percentages Most healthcare statistics are reported as decimals If the digit in the first decimal place is less than 5, leave the whole number as it is If the digit is 5 or more, round up to the next whole number. For example, 14.4 = 14; 17.6 = 18 ©2006 All rights reserved.

Mathematics Review Rounding Decimals If you need to “carry out” the number to one decimal place, the basic rule is to go up two and down one For example, 14.46 = 14.5; 14.13 = 14.1 Notice in 14.46 – we went out two decimal places to .46, then round down to .5 because the 6 in .46 is greater than 5 In 14.13, notice that the 3 in .13 is not over 5, therefore, we do not round up, but rather keep the .1 If you are required to carry the decimal points out two places, the division process then should be carried out to one more place in the quotient and rounded back ©2006 All rights reserved.

Mathematics Review Percentage as a Type of Ratio The ratio of a part to the whole is often expressed as a percentage A percentage is a fraction expressed in hundredths For example 34% means 34/100 This is a useful way to make fair comparisons Not all percentages are converted to whole numbers For example 1/8 = .125 = 12.5% ©2006 All rights reserved.

Mathematics Review Changing a fraction to a percentage For example: ½ Divide the numerator by the denominator Divide 1 by 2 which equals 0.5 Then multiply by 100, because you need to convert this to hundredths 1/2 converts to 50% ©2006 All rights reserved.

Mathematics Review Changing a decimal to a percentage For example: 0.29 Multiply the decimal by 100 0.29 x 100 = 29% ©2006 All rights reserved.

Mathematics Review Changing a percentage to a fraction Eliminate the percent sign and multiply the number by 1/100 For example: 5% Multiply 5 x 1/100 = 5/100 Convert the fraction to its simplest form Both 5 and 100 can be divided by 5 5 divided by 5 = 1 100 divided by 5 = 20 5/100 = 1/20 ©2006 All rights reserved.

Mathematics Review Changing a percentage to a decimal Eliminate the percent sign and place a decimal point two places to the left If the percentage is only one digit, place a 0 in front of it and place the decimal point in front of the 0 76% = .76 4% = .04 104% = 1.04 ©2006 All rights reserved.

Mathematics Review Calculating Ratio Ratio is calculated by dividing one quantity by another The number can be greater than 1 or less than 1 For example, if seven men and five women were in a group, the ratio of men to women would be 7/5 or this may be written as 7:5 and is verbalized as 7 to 5 The numbers 7 and 5 have no common factors so you cannot simplify the ratio However, suppose there are 6 men and 10 women in a group The ratio is now 6:10 The numbers in this ratio do have a common factor of 2, so you can simplify this ratio by dividing each number by 2 The ratio in this case would be 3:5 ©2006 All rights reserved.

Mathematics Review Proportion as a Type of Ratio A particular type of ratio A proportion is a ratio in which x is a portion of the whole, x + y In a proportion, the numerator is always included in the denominator For example, if two women out of a group of ten over the age of 50 have had cancer, where x = 2 (women who have cancer); and y = 8 (women who do not have cancer); the calculation would be 2/(2 + 8) = 0.2 The proportion of women that have cancer is 0.2 ©2006 All rights reserved.

Mathematics Review Rate as Type of Ratio A ratio in which there is a distinct relationship between numerator and denominator and the denominator often implies a large base population A measure of time is often an intrinsic part of the denominator Careful attention should be given to rates and percentages Errors can occur due to misplaced decimal points The term rate is often used loosely to refer to rate, proportion, percentage, and ratio ©2006 All rights reserved.

Mathematics Review Calculating Rate The basic rule of thumb for calculating rate is to indicate the number of times that something actually happened in relation to the number of times that something could have happened (actual/potential) Formula Rate = Part/Base or R = P/B ©2006 All rights reserved.

Mathematics Review Average The values obtained by dividing the sum of a set of numbers by the number of values ©2006 All rights reserved.