C784 Final Exam Study Notes on Healthcare Statistics | Accurate & Verified Answers to Pass Actual Exam

C784 Final Exam Study Notes on Healthcare Statistics | Accurate & Verified Answers to

Pass Actual Exam


Healthcare Statistics - C784

Before we begin numerical operations, it is important to recognize that there
are different number systems. The different systems are nested within one
another, so the "smallest" system of whole numbers is contained in a larger
system of integers which in turn is part of an even larger system of rational
numbers. The rational numbers are then part of the "largest" number
system, the real numbers.

Awhole number*isanumberthatwearefamiliarwithfromgradeschool.These
numbersare:
0,1,2,3,4,5,6,7,8,9,...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."

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:




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.)

Rational numbers*are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=414=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,−3101-3101indecimalformis−0.02970297...-0.02970297...,which
wecanalsowriteas0.0297¯¯¯¯¯¯¯0.0297¯(withbarabove02970297)which
meansthe02970297continuesrepeatingforever.

,Real numbers*+are the numbers that can be placed on a number line. One
important component of numeracy is the ability to understand the value of a
number at a glance. A way to demonstrate this understanding is to be able
to place a number (roughly) on a number line.
Whole numbers*+of+1616,+11,+30243024, and+55+can be placed in
numeric order from least to greatest:+11,+55,+1616,+30243024. We
apply this same concept when using a number line. The numbers
increase as you go to the right on the number line.
To place a whole number on a number line, you put a dot or line at the place
of the value. For example, we have placed a dot above+22+on the number
line below.
You can use a similar strategy for placing+integers*+on the number line.
Remember, however, that for negative integers, the value is smaller the
farther from zero.

,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,+4.34.3+should be placed on the number line between+44+and+55,
not between+44+and+33. Likewise+134134+is+greater than+11+and therefore
between the integers+11+and+22.




Negative fractions and decimals can be placed between negative integers
the same way, though remember that the lesser value integer will be to
the+left+of the greater integer.+For negative numbers, the farther away from
zero, the smaller the value.




In mathematics, a collection of numbers is referred to as a+set*. In statistics,
a collection of numbers is often referred to as+data*. These groups of
numbers and data can be categorized as+discrete*+or+continuous*.

A collection of numbers is+discrete+if its values are distinct, separate, and
unconnected. If the values within the set are connected, without gaps, the
collection is considered to be+continuous. This may seem overly abstract.
To visualize this concept, refer to the number line below.




An 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+11+and+22+is called an+interval*.
The set of+real numbers*+between+11+and+22, highlighted green in the
above number line, is a continuous set. This set contains all numbers within
the interval; there are no gaps in values. The values within the set are
connected, without gaps.

, A set of data is+continuous+if it can hold any value within the set. An
example of continuous data might be age. It is possible to
be+22.6722.67+years old. Real numbers are considered continuous.
Looking at another set of data, consider the number of cars someone owns.
It is not possible to own+3.43.4+cars; you either own three cars or four. The
number of cars someone owns is an example of a discrete set of data, since
the values are distinct, separate, and unconnected. Positive+integers*+are
an example of discrete data.
DISCRETE

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.

CONTINUOUS


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.

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.