Statistics Week 3 MATH REVIEW

To convert a percentage to a decimal,

eliminate the percent sign and place a decimal point two places to the left of the decimal point. If the percentage is only one digit, place a 0 in front of it and place the decimal point in front of the 0. For example: 76% would be .76 4% would be .04 104% would be 1.04

A fraction

is a fragment or one or more parts of a whole. It is designated by placing one number over another number such as 6/7. The top number in a fraction is called the numerator and the bottom number is the denominator. When 6 is divided by 7 the resulting number is called a quotient.

Rounding

is a process of approximating a number. The primary reason for rounding is to obtain a useable number. Numbers may be rounded to the nearest 10, 100, and so on. This is a critical part of your learning for this semester - so please make sure you have a firm grasp of rounding.

A proportion

is a relationship of one portion to another or to the whole or of one thing to another. A proportion is a ratio in which the elements in the numerator must also be included in the denominator. For example, if two women out of a group of ten over the age of 50 have had ovarian cancer, x = 2 (women who have had ovarian cancer) and y = 8 (women who have not had ovarian cancer), the calculation would be 2 divided by 10. x / ( x + y ) = 2 / (2 + 8) = 0.2

An average is the value obtained by dividing the sum of a set of numbers by the number of values.

Average is generally referred to as the arithmetic mean to distinguish it from the mode or median. These terms will be discussed in a future lesson. Formula to Compute an Average: Add (summate) all scores in a distribution and divide by the number of scores (N) in the distribution. Scenario: Let's say that you've taken six Health and Wellness tests. Your scores are 82, 78, 94, 56, 91, and 85. Adding together the scores gives you a total score of 486. Now, divide this by 6 (the number of tests you have taken). This equals 81. This means that your average score on Health and Wellness tests is an 81.

HIM Computational Applications

Departmental Health Information Management (HIM) managers apply basic mathematics when determining labor costs, deciding on equipment purchases or leases, computing productivity, and making staffing decisions. These are all factors relevant to the budgeting process.

A decimal point notation indicates a value that is less than one (1).

In 14.37, for example, the digits to the right of the decimal point (3 and 7) are called decimal digits. The decimal point is used to separate the fraction of the whole number (.37) from the whole number itself (14). The decimal point is not ordinarily used in whole numbers (for example, 14.0) unless the healthcare facility has a particular reason for doing so. Tip : The decimal .5 is usually written as 0.5 in order to call attention to the decimal point.

A rate has many meanings.

It is a value or price (as in 50 cents a pound). It is a unit of something (as in the rate of speed is 30 mph or the birthrate is 20 births per every 100 teenagers or the interest is 8.6% It is expressed as a percentage. A rate is a ratio in which there is a distinct relationship between the numerator and the denominator and the denominator often implies a large base population. A measure of time is often an intrinsic part of the denominator. Healthcare facilities calculate many types of rates in order to determine how the facilities are performing. The basic rule of thumb for calculating rate is to indicate the number of times something actually happened in relation to the number of times it could have happened (actual/potential). For example, let's say you have been eating out at restaurants often in the last few weeks. To calculate the rate of meals you have eaten out in one week, divide the number of meals you actually ate out (say, 13) by the number of meals you could have eaten out (21). The rate is 13/21, or 61.9%. The formula for determining rate is as follows: Rate = Part/Base, or R= P/B

Converting to Other Units of Measure

It may be necessary to convert data from U.S standards of measure to metric units or vice versa. When analyzing data, it is important that data be reported in the same units.

Rounding Decimals for Healthcare Statistics

Most healthcare statistics are reported as decimals, and each healthcare facility has its own policy on the number of decimal places to be used in computing and reporting percentages. The principles that apply to rounding whole numbers also apply to rounding decimals. To round to the nearest whole number, look at the first digit to the right of the decimal point (tenths); if the number is 5 or more, the whole number should be rounded up; if the number is less than 5, the whole number should be left as it is. Thus, the whole number in 14.4 should remain at 14; however, 14.5 should be rounded up to 15. To round to the nearest tenth, you do the same thing except use the hundredths digit rather than the tenth. The hundredths is the second digit to the right of the decimal point. For example, 14.46 would be rounded up one to 14.5 because the 6 in .46 is greater than 5. In the case of 14.13, the 3 in .13 is less than 5, so the .1 is kept rather than rounding up. To round to the nearest hundredths, the calculation must be carried out to three decimal places (the thousandths digit) and then rounded. For example, 14.657 would be rounded to 14.66 because the 7 in .657 is greater than 5. In the case of 14.654, the 4 in .654 is less than 5, so the .65 is kept rather than rounding up. Tip : When the decimal points must be carried out to two places, the calculation should be carried out to one more place (the third place) in the quotient and then rounded back. 1/7 = 14.28 6 = 14.29 Tip : Do not round anything until the final answer for any calculation.

Rounding to the Nearest Hundred

Rounding to the nearest hundred refers to rounding numbers that fall between multiples of 100. For example, 327 falls between 300 and 400 but is close to 300. The 2 in the tens place indicates that 327 should be rounded down to 300.

Rounding to the Nearest Ten

Rounding to the nearest ten means that any number between multiples of ten (10, 20, 30, 40, and so on) is rounded to the multiple it is closest to. For example, 31 falls between 30 and 40 but is closest to 30, so it is rounded to 30. However, 37 is closer to 40 so it is rounded to 40. When a number is exactly between the two multiples of ten, the rule of thumb is to round up. In other words - the 5 in the ones place indicates that 35 would be rounded up to 40.

A quotient may also be expressed in decimals.

Scenario : The fourteen (14) members of your graduating health information class decide to participate in OTC's Information Day. The booth is going to be open for twenty-one (21) hours over a three-day period. To find out how many hours each student would need to attend to the booth, you would divide the numerator (21 hours) by the denominator (14 students). This calculation gives a quotient of 1.5. Thus, each student would have to attend to the booth for 1.5 hours over the three-day event.

Values of fractions can be increased or decreased. Fractions should be reduced to their lowest form

This is achieved by dividing both the numerator (also called a dividend) and denominator (also called a divisor) by a common number that is able to be divided by both. 5/10 can be reduced by dividing both by 5, which = ½. When answering questions in this class it is expected that fractions will be reduced to their lowest form.

Ratio

Three general classes of mathematical parameters are used to relate the number of cases, patients, or outcomes in the healthcare environment to the size of the source population in which they occur. The most basic measure is the ratio. A ratio is a relationship or comparison between two different things or one number to another. Ratios are generally reported by a fraction or numbers side by side separated by a colon (8:10 reads 8 out of 10) A ratio can be reduced to its lowest equivalent so that 8 out of 10 is equivalent to 4 out of 5. For example, if a group consisted of seven men and five women, the ratio of men to women would be 7/5. This ratio will be written as 7:5 and verbalized as 7 to 5. All rules that apply to fractions apply equally to ratios. The numbers 7 and 5 have no common factors, so this ratio cannot be simplified. The formula for ratio is simply x/y , with x representing men and y representing women in the above examples. If the ratio of women to men is being expressed, the formula would be y/x , with 5/3 and 5:3 verbalized as 5 to 3.

To change a fraction to a percentage

divide the numerator by the denominator and multiply by 100 and add a percent sign. For example, to change 1/2 to a percentage, divide 1 by 2 and multiply by 100. The calculation is as follows: 1/2 = 0.5 x 100 = 50% To convert 60/80 to a percent - divide 60 by 80 and then multiply quotient by 100. (60/80) = 75 then multiply by 100= 75%

To convert a percentage to a fraction,

eliminate the percent sign and multiply the number by 1/100. A simpler version of this is to place the percentage number in the numerator and 100 in the denominator and convert to the lowest fraction. For example: 5% would be 5 x 1/100 = 5/100 15% would be 15 x 1/100 = 15/100 Fractions are usually converted to their simplest form (required in this class). In the example of 5%, both 5 and 100 can be divided by 5, which would result in a fraction of 1/20. In the example 15%, both 15 and 100 are again divisible by 5, resulting in a fraction of 3/20. Another example - to convert 55% to a fraction: Eliminate the percent sign 55 becomes the numerator and 100 is the denominator Convert to the lowest (55 and 100 can both be divided by 5 55/5 divided by 100/5 = 11/20 (lowest fraction)

percentage

is the number of times something happens out of every one hundred times and is expressed as a specific number followed by a percent sign (%). A percentage indicates the proportion of a whole. To convert a decimal to a percentage multiply the decimal by 100. It is also considered a fraction that is expressed in hundredths. For example, the fraction 34/100 would be written .34 as a percentage. Percentages are a useful way to make fair comparisons. For example, if 20 patients died in Hospital A last month and 50 patients died in Hospital B during the same period, one might conclude that it would be better to use the services of Hospital A because Hospital A had fewer deaths. However, that conclusion would be wrong if Hospital A had 100 discharges during the month and Hospital B had 500 discharges for the same period. (Hospital A had a death rate of 20%, which Hospital B's death rate was only 10%.) It is expected that % signs will be used when calculating formulae.

"Corrected to"

is the term used to indicate the degree to which the answer should be specified. Seldom will data be specified beyond one or two decimal places. If the last digit is five or greater, the preceding number should be increased one digit. If the last digit is less than five, the preceding number remains the same.

"Carried to"

is the term used to indicate what decimal place or whole number the quotient is to be determined, in order to round the data to the specified number. If it is stated that the answer is to be correct to two decimal places, the quotient should be carried out to at least three places. If the answer is to be correct to the nearest whole number, the answer must be carried to one decimal place.

To convert a decimal to a percentage

simply multiply by 100 (which moves the decimal point two laces to the right) and add a percent sign. 0.49 = 49 = add percent (%) = 49% Another way: To change a decimal to a percentage, simply multiply the decimal by 100. The calculation changes the position of the decimal. For example: 0.29 x 100 = 29%