Calculating & Reporting Healthcare Statistics Second Edition Chapter 2 Mathematics Review

Calculating & Reporting Healthcare Statistics

Second Edition

Chapter 2Mathematics Review

©2006 All rights reserved.

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


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


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


Mathematics Review• Rounding Whole Numbers

– 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


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


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


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


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%


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%


Mathematics Review

• Changing a decimal to a percentage

• For example: 0.29– Multiply the decimal by 100– 0.29 x 100 = 29%


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


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


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


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


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


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


Mathematics Review

• Average– The values obtained by dividing the sum of a

set of numbers by the number of values

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Calculating & Reporting Healthcare Statistics Second Edition Chapter 2 Mathematics Review