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Calculating Healthcare Statistics Math Review
1.
© 2019 AHIMA ahima.orgahima.org Calculating
and Reporting Healthcare Statistics, Sixth Edition Chapter 2: Mathematics Review
2.
© 2019 AHIMA ahima.org Learning
Objectives • Calculate using decimals, ratios, proportions, rates, and percentages • Differentiate between a numerator and denominator • Perform rounding whole numbers and decimals • Determine the proper conversion of fractions and decimals to percentages • Compute the average or mean 2
3.
© 2019 AHIMA ahima.org 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 • Example: 3 5 • 3 is the numerator • 5 is the denominator
4.
© 2019 AHIMA ahima.org Quotient •
The number obtained by dividing the numerator of a fraction by the denominator • May be expressed in decimals • Example: 3 5 = 0.6 • 0.6 is a quotient
5.
© 2019 AHIMA ahima.org 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 fraction parts • The decimal .5 is usually written as 0.5 in order to call attention to the decimal point
6.
© 2019 AHIMA ahima.org Decimal
Places
7.
© 2019 AHIMA ahima.org Rounding
Whole Numbers • A process of approximating a number • One way of approximating is to round the number to the nearest 10, 100, etc.
8.
© 2019 AHIMA ahima.org 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 • If 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 up to 40 • Anything between 34 and 31 would be rounded down to 30
9.
© 2019 AHIMA ahima.org Rounding
to The Nearest Hundred • Refers to rounding numbers that fall between multiples of 100 • 327 is between 300 and 400 • The 2 in the tens place indicates we should round down to 300 • 7,868 is between 7,800 and 7,900 • The 6 in the tens place indicates we should round up to 7,900 • When the last two numbers are exactly between two multiples of 100, the rule of thumb is to round up; 350 would be rounded to 400.
10.
© 2019 AHIMA ahima.org Rounding
to The Nearest Thousand • Refers to rounding numbers that fall between multiples of 1,000 • We must look at the last three digits. • If the last three digits are 449 or less, then the number is rounded down; in the number 7,337, the 337 indicates that 7,337 should be rounded down to 7,000
11.
© 2019 AHIMA ahima.org Rounding
to The Nearest Thousand (continued) • The number 7,868 falls between 7,800 and 7,900. In this case, the 868 indicates that 7,868 should be rounded up to 7,900 • If the last three numbers are exactly between two multiples of 1,000, the rule of thumb is to round up; 7,500 would be rounded up to 8,000.
12.
© 2019 AHIMA ahima.org 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; 14.5 = 15
13.
© 2019 AHIMA ahima.org Rounding
Decimals (continued) • If you need to “carry out” the number, round based on the number one decimal place to the right of the decimal places needed • For example, when rounding to one decimal place: 14.46... = 14.5; 14.13... = 14.1 • Notice in 14.46..., we rounded up 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 rounded down, to .1
14.
© 2019 AHIMA ahima.org Percentages •
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 = 0.125 = 12.5%
15.
© 2019 AHIMA ahima.org Changing
a Fraction to a Percentage • Divide the numerator by the denominator and multiply by 100 • The term ‘percent’ may be interpreted as ‘per one hundred’ • For example: ½ • Divide 1 by 2 which equals 0.5 • Then multiply by 100, because you need to convert this ‘per one hundred’ • 1/2= 0.5 x 100 = 50%
16.
© 2019 AHIMA ahima.org Changing
a Decimal to a Percentage • Multiply the decimal by 100 • For example: 0.29 • 0.29 × 100 = 29%
17.
© 2019 AHIMA ahima.org Changing
a Percentage to a Fraction • Eliminate the percent sign and multiply the number by 1/100 • For example: 5% • 5% = 5 × 1/100 = 5/100 • Fractions are usually converted to their simplest form • In the example of 5 percent, both 5 and 100 can be divided by 5, which would result in a fraction of 1/20
18.
© 2019 AHIMA ahima.org Changing
a Percentage to a Decimal • Eliminate the percent sign and place decimal point two places to the left • For example: 76% = 0.76 • If the percentage is only one digit, place a 0 in front of the number and place the decimal point in front of the 0 • For example: 4% = 0.04
19.
© 2019 AHIMA ahima.org Calculating
Ratio • A ratio expresses the relationship of one quantity to another. • 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 • Ratios should be simplified to simplest form. • 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
20.
© 2019 AHIMA ahima.org Proportion •
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
21.
© 2019 AHIMA ahima.org Rate •
A rate is 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
22.
© 2019 AHIMA ahima.org 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
23.
© 2019 AHIMA ahima.org Averages •
An average is the value obtained by dividing the sum of a set of numbers by the number of values • Also referred to as the mean • For example: • If a student took six tests in a particular class and the scores are 82, 78, 94, 56, 91, and 85 • Added together these equal 486 • Divide 486 by 6 = 81 • The student’s average score is 81
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