module 1 statistic

The symbol > means

"greater than" and also displays the opposite relationship between the entities. The open portion of the symbol always points to the larger quantity. The pointed side of the inequality always shows the lesser value, whether it is on the right or left.

The symbol < means

"less than" and shows that the value or variable to the left is less than the value or variable to the right.

Display x>−2 using interval notation.

(−2,∞)

Display −5<x<−2 using interval notation.

(−5,−2)

Display x≤8 using interval notation.

(−∞,8] The sign inside the written interval essentially discloses whether the interval, x , is less than or greater than the value. The infinity symbol is also always paired with a parenthesis, rather than a bracket.

Which of the following is the correct translation of 10>x>6 ?

10 is greater than x which is greater than 6

What kind of number is 51 ?

3×17=51 , so 51 is a composite number.

How would " w is less than or equal to 9 , but greater than or equal to 5 " be written?

9≥w≥5

discrete

A collection of numbers is discrete if its values are distinct, separate, and unconnected.

factor tree

A factor tree showing how 30 is broken down into its factors. 3 X 10 is the starting equation, and 10 is further broken down into its factors of 2 X 5. 3 is already its own prime factor. The resulting equation is 3 X 2 X 5 =30

In Writing

A parenthesis, ( , denotes that the value alongside it is not to be included (as in < and > ). A bracket, ] , means that the value alongside it is included (as in ≤ and ≥ ). Use a comma between the two values to represent the interval. So how would we write 4<x≤9 with x being our interval? Place the lower boundary on the left and the upper boundary on the right: 4 , 9 . Use an open parenthesis before the 4 to represent greater than, and a closed bracket after the 9 to represent less than or equal to: (4,9] .

Advantages and Disadvantages of Estimation

Advantages Estimations can often provide quicker calculations. They can offer a more "global" picture of the situation. They can get results in the absence of information. Each patient visit takes 8 -and-a-half minutes. There are 21 patients on the floor. Will you finish the round in your 4 -hour shift? If you estimate 10 minutes per patient and 20 patients, you will estimate that the round will take around 200 minutes. Considering that 180 minutes =3 hours, you will get a quick answer to your "yes or no" question. The hospital is using a new data entry system. You do not know how much time this will add to each round, so you have to estimate, and you think it is 3 more minutes per patient. Given that you have 20 patients, 20×3=60 means that this new data system will add an extra hour to your work. You now have a more "global" sense of what this change means for your workday.

composite number

All integers are either prime or composite. A composite number* has at least one positive factor other than 1 and itself. For example, 10 can be divided evenly by 1,2,5, and by 10 . It has positive factors other than 1 and itself: 2 and 5 are positive factors of 10 .

distribution

An entire set of data can also be categorized as discrete or continuous. If a distribution* turns out to have a defined number of outcomes, the distribution is considered discrete. If the distribution results in any number of outcomes in an interval, it is considered continuous.

On a Number Line

An open circle denotes that the value is not to be included (as in < and > ). A closed circle means that the value is included (as in ≤ and ≥ ). Connect the plotted values on the number line to represent the interval.

bsa

Body surface area (BSA) may be used to figure medication dosages, specifically for infants and children. Body surface area (BSA) may also be used to figure dosages for patients with severe burns and renal failure. Although the healthcare provider will be prescribing the medications, the nurse is responsible for verifying that the dosages ordered are within dosage guidelines. There are several formulas to figure body surface area. The formula most commonly used by nurses requires an understanding of how to utilize a square root. The nurse must know that patient's height and weight. The specific formula used will depend on if the height and weight is in pounds and inches or in meters and kilograms. Body Surface Area (BSA) Using Pounds and Inches This is the formula using pounds and inches. BSA(m2)=Height (in) × Weight (lbs)3131−−−−−−−−−−−−−−−−−−−−−−−−√ Body Surface Area (BSA) Using Centimeters and Kilograms BSA(m2)=Height (cm) × Weight (kg)3600−−−−−−−−−−−−−−−−−−−−−−−−−√ Example An example would be calculating the BSA for an infant who is 60 centimeters long and weighs 3.5 kg BSA(m2)=60 cm × 3.5 kg3600−−−−−−−−−−−−−−√

continuous definitrion and explanation

Can have any value within an interval Is "measured" Does not have clear boundaries between elements or data points In mathematics, the set of real numbers is an example of a continuous set. This sets contains continuous elements, with no discernible gaps between each element. Remember that the number line is a visual representation of the set of real numbers. Just as the number line is continuous with no gaps, so is the set of real numbers. In statistics, some data sets will be continuous. Examples of continuous data sets are temperature, distance, and time, as the set of possible values within these groups is continuous. An element in these groups can hold any real number within a certain interval, dependent upon the scale used.

discrete definition and explanation

Can only have certain, distinct values Is "counted" Contains unconnected points In mathematics, whole numbers, integers, and even integers are all examples of discrete sets. These sets contain unconnected elements, with gaps between each value. In statistics, some data sets will be discrete. Examples of discrete data sets are the number of adults in a household, the results of rolling two dice, and number of machines in operation, as these are distinct groups.

During a physical, the nurse records the patient's age, weight, and height. Are these data discrete or continuous?

Continuous Correct. The answer is b. These are all continuous measurements for which it is possible to have fractional parts.

disadvantage

Disadvantages Estimations are not accurate. Therefore, they cannot be used for calculations that need to be precise. They can be further off than the estimator realizes, leading to wrong conclusions. Sometimes the exact numbers are just as easy to calculate. Medication dosages, for example, should not be estimated, but rather given in exact measurements. If there are 23 patients on a floor and each patient takes 12 minutes rather than 8 -and-a-half minutes, your quick estimate of 200 minutes will be off by 76 minutes, and you will not be finishing on time. If you are going to punch numbers into a calculator, it is often just as easy to punch in the exact numbers to get an accurate answer. The estimation does not save time.

A graph shows the efficacy of a particular drug at different dosages. Is this data discrete or continuous?

Discrete Correct. The answer is a. The graph shows discrete drug dosages, not all possible dosages, between two numbers.

When evaluating an expression, Order of Operations prompts us to:

First do all operations that lie inside parentheses*. Next, do any work with exponents* or roots. Working from left to right, do all multiplication* and division*. Finally, working from left to right, do all addition* and subtraction*.

continuous

If the values within the set are connected, without gaps, the collection is considered to be continuous

negative integer in personal finance

Negative numbers are used in finance to show a negative amount of money, often representing a debt. A negative amount of money indicates that there is less than $0 , or in other words, that money is owed. How is it possible to have negative money? Let's look at an example: Alison's current bank account balance is $1,200 . This amount is positive, as she has more than $0 . Alison withdraws $1,300 . Her account balance is now $1,200 - $1,300 , which equals −$100 . This amount is negative, as she now has less than $0 in the bank. In other words, she owes the bank $100 . This is known as an overdraft, which has resulted in her account being overdrawn

PEMDAS

PEMDAS is a common acronym used to describe the order in which mathematical expressions should be performed. Many people find it helpful to use a mnemonic to remember "PEMDAS" as the following graphic illustrates.

prime factorization

Prime factorization* is the act of identifying which prime factors make up a particular composite number. Below we will learn a method for performing prime factorization. Prime factorization is essentially the Fundamental Theorem of Arithmetic at work.

What kind of number is 47 ?

The answer is a. 47 is a prime number because it has no factors other than 1 and itself.

Timesheets log the days that a nurse works each week. Does the week's timesheet give data that is discrete or continuous?

The answer is a. The days of the week are discrete and do not allow for values between them. discrete

What kind of number is 27 ?

The answer is b. 27 is a composite number because it has the factors 1,3,9,27 .

According to the strictest definition, −1/3 is...

The answer is b. According to the strictest definition, −1/3 is a rational number because it can be represented as a fraction.

According to the strictest definition, 0.07 is

The answer is c. 0.07 is a decimal that ends and therefore a rational number because it can be written as a fraction.

π is...

The answer is d. π is a real number whose complete decimal expansion goes on forever and does not repeat.

-17

The answer is d. −17 is an integer, and all integers are also rational numbers, which in turn are real numbers.

The fact that the sum of a number and 0 will always equal the number is calle

The identity property

negative integer in sports

There are a variety of sports statistics that use negative numbers. In races, such as track or auto racing, negative numbers are used in times to show time behind or ahead. Ice hockey and soccer use a statistic called goal differential. Goal differential measures the difference between a team's goals and the opposing team's goals. For example: L.A. is playing D.C. in a two-game series. In Game One, L.A. scores 3 goals, and D.C. scores 1 goal, giving L.A. a goal differential of 3−1 , which equals +2 . Here, a plus sign is used to show that the goal differential is positive: L.A. has a goal differential greater than 0 because they scored more goals than their opponent. In Game Two, L.A. scores 1 goal, but D.C. scores 4 goals, giving L.A. a goal differential of 1−4 , which equals −3 . Here, a minus sign is used to show that the goal differential is negative: L.A. has a goal differential less than 0 because they scored fewer goals than their opponent.

negative integer in temperature

There are many different scales used to measure temperature, including Kelvin, Celsius, and Fahrenheit. Outside of the formal sciences, Fahrenheit (°F) is the most commonly used temperature scale in the United States. On this scale, negative numbers are used to show a temperature that is less than 0° F. For example: It is a cold winter night in Minneapolis: the temperature is 5° F. This value is positive, as the temperature is greater than 0° F. The temperature then drops by 8° F. The temperature in Minneapolis is now 5° F - 8° F, which equals −3° F. This value is negative, as the temperature is now less than 0° F.

The radical sign refers to the negative square root of a real number. True or false?

This is a false statement. The radical sign refers to the principal square root.

Every positive whole number has two square roots. True or false?

This is a true statement. Every whole number has both a principal and a negative square root.

0 , 1, 2 is a set of continuous data. True or False?

This statement is false. 0 , 1 , and 2 are distinct consecutive integers. There are numbers, such as 1.5 , between them, so they are not continuous.

True or False? A prime number has only itself as a factor.

This statement is false. 1 is also a factor of every number, prime or composite.

True or False? Any integer is also a whole number

This statement is false. An integer can be negative, such as the number −100 . −100 is not a whole number.

True or False? Two composite numbers can have exactly the same factors.

This statement is false. Every composite number has a unique factorization

Temperature is an example of continuous data. True or False?

This statement is true. Temperature covers an entire interval of data and can be "measured" rather than counted, so it is continuous.

you first complete any operations that lie inside parentheses*.

When more than one set of parentheses appear directly next to each other, they're being used to dictate in what order operations should be performed. For example, we know that (3+5)×2 means we should first perform 3+5 , and then multiply that sum by 2 . Similarly, if we have ((3+5)÷4)×2 , we must first add 3+5 , then divide by 4 , then multiply by 2 . Parentheses must always be closed, which is why on the left side of the expression, there are two left parentheses — one to close the 3+5 expression and one to close the ÷4 expression. ((3+5)÷4)×2

creating factor tree

Write the number at the top Find one factor of the number. It can be any factor. Draw two lines from the number and then write the factor and the quotient when the number being factorized is divided by its factor. In the example above, 3 divides 30 ten times. So " 3×10 " is the first line of the factor tree. Examine the two factors you have written. Are either of them composite? If so, draw two lines to that factor and find its factors. For example, 3 is a prime number. It cannot be further factored. However, 10 is a composite number and needs to be further factored. Repeat the process above until you have only prime factors in the bottom rows

Display −1≤x≤3 using interval notation.

[−1,3]

Negative integers

are denoted by a minus sign directly in front of the integer. For example, " −5 " is read as "negative five." Here are some examples of negative integers: −1,−2,−3,−4,−5,−6,−7,−8,−9,..

n statistics, a collection of numbers is often referred to as

data-These groups of numbers and data can be categorized as discrete* or continuous*.

Positive integers

have a value that is greater than zero (meaning to the right of 0 on the number line), while negative integers are less than zero (or to the left of 0 on the number line). It is important to remember that zero is neither positive nor negative. (However, zero is considered an integer.) Positive integers include: 1,2,3,4,5,6,7,8,9,...

interval

interval is a set of numbers between two specified values. An interval can be visualized as a segment of the number line. The segment of the number line above that falls between 1 and 2 is called an interval*.

factors*

is intertwined with divisibility. Factors are integers that evenly divide the initial integer. When multiplied together, the product of these factors give you that initial integer. For example 6×5=30 . 30÷5=6 . Because 5 divides 30 without a remainder, 5 is a factor of 30 . 6 is likewise a factor of 30 .

Integers*,

like whole numbers, are numerical figures that do not contain a fractional or decimal component. Integers, unlike whole numbers, can be either a positive number*, a negative number*, or zero. The following number line displays integers: Number line displaying integers, which includes both negative and positive whole numbers. Positive integers have a value that is greater than zero (meaning to the right of 0 on the number line), while negative integers are less than zero (or to the left of 0 on the number line). It is important to remember that zero is neither positive nor negative. (However, zero is considered an integer.)

-36

negative integer

-4

negative integer in addition to a rational and real

whole number*

number that we are familiar with from grade school. These numbers are: 0,1,2,3,4,5,6,7,8,9,... As the name indicates, "whole" numbers are numbers whose values are "whole," such as 1 or 2 . Fractions or decimals, on the other hand, can be "parts of a whole," such as "one half." Whole numbers can be represented without a fractional or decimal component and are not negative.

Rational numbers*

numbers that can be expressed as a fraction. This class of numbers includes all integers since any integer can be expressed as a fraction: 4=41 Rational numbers are also decimal numbers that have expansions that end or continue to repeat forever, rather than continuing forever without repeating. For example, −3101 in decimal form is −0.02970297... , which we can also write as 0.0297¯¯¯¯¯¯¯ (with bar above 0297 ) which means the 0297 continues repeating forever.

111

positive integer

45

positive integer in addition to being a rational and real number

prime numbers

prime number* is a positive integer with exactly two positive factors*, 1 and itself; it cannot be divided evenly by any other two integers. For example, the only positive numbers that divide 3 are 1 and 3 . Therefore, 3 is a prime number. Prime numbers play an important role in factoring, which we will explore later in this module. Examples of Prime Numbers: Positive factors of 2 : 1,2 Positive factors of 7 : 1,7 Positive factors of 11 : 1,11 Positive factors of 23 : 1,23

-1.6

rational number

1/4

rational number

0.675

rational number in addition to being a real number because it is a decimal whose expansion ends

8 2/3

rational number in addition to being a real number because it is a fraction

12.25

rational number in addition to real number it is a decimal whose expansion ends

sympol of pie

real number

real numbers*

real number is any number that can be placed on the number line, whether that be negative or positive, fraction or decimal. Real numbers also include decimals that do not end and cannot be written as a fraction. An example of this is pi (sometimes written as π ). Pi is approximated to 3.14 , but the decimals do not end and do not repeat. Everything included on the number line below is considered a real number:

Placing a rational number* on the number line

requires recognizing that any partial amount in a fraction or decimal makes the number greater than the whole number part of the fraction or decimal. For example, 4.3 should be placed on the number line between 4 and 5 , not between 4 and 3 . Likewise 134 is greater than 1 and therefore between the integers 1 and 2 .

In mathematics, a collection of numbers is referred to as a

set

Fundamental Theorem of Arithmetic*

states that all composite numbers* can be represented as the product of prime numbers*. It is important to be able to find the prime factors of any composite number. Fundamental Theorem of Arithmetic This theory simply states that any integer greater than 1 is either prime, or is the product of prime numbers.

Which of the following is the correct translation of 8<z≤16 ?

z is greater than 8 , but less than or equal to 16

Which of the following is the correct translation of −3<y<4 ?

−3 is less than y which is less than 4

How would " x is greater than or equal to −4 , and less than 7 " be written?

−4≤x<7