Understanding Healthcare Stats: Real Numbers, Discrete & Continuous Data, Operations | Exams Advanced Education | Docsity (2024)

Download Understanding Healthcare Stats: Real Numbers, Discrete & Continuous Data, Operations and more Exams Advanced Education in PDF only on Docsity! C784-Applied Healthcare Statistics complete questions and answers Rational number (aka 'fractional') Numbers that can be expressed as a fraction Integers Solid positive and negative numbers Real Numbers A real number is any number that can be placed on the number line, whether that be negative or positive, fraction or decimal. 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. −100-100 is not a whole number. Read all the options before answering. −17-17 is... (a. an integer b. a rational number c. a real number d. all of the above.) d. all of the above. −17-17 is an integer, and all integers are also rational numbers, which in turn are real numbers. set In mathematics, a collection of numbers is referred to as a set* Interval 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*. Discrete data 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. (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.) Continuous data 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. (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.) 00, 11, 22 is a set of continuous data. True or False? False. This statement is false. 00, 11, and 22 are distinct consecutive integers. There are numbers, such as 1.51.5, between them, so they are not continuous. emperature 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. Timesheets log the days that a nurse works each week. Does the week's timesheet give data that is discrete or continuous? Discrete. The days of the week are discrete and do not allow for values between them. A graph shows the efficacy of a particular drug at different dosages. Is this data discrete or continuous? Discrete. The graph shows discrete drug dosages, not all possible dosages, between two numbers. So: 64 divided 2 * 3 = Work it Left to right 64 divided by 2 = 32 x 3 = 96 A ??? is a positive integer with exactly two positive factors*, 11 and itself; it cannot be divided evenly by any other two integers. For example, the only positive numbers that divide 33 are 11 and 33. Therefore, 33 is a prime number. Prime numbers play an important role in factoring, which we will explore later in this module. prime number prime numbers, only 1 and itself like 29 It is a prime number. Prime numbers are always odd Composite number 15--can divide by 1, 3, 5 so it is composite 2, 3, 5, 7 are all what type of numbers Prime Prime factorization Breaking down a composite number until all of the factors are prime (like 9 is 3 and 9 ) Mean values The mean* is one of the most useful measures of central tendency. The mean, also known as the average, is a single value that represents the center of a set of data values. Mean can be substantially influenced by one or more extreme values in a data set (think skewed data), so mean is only used when the data is symmetric. Therefore, we say that the mean is not a resistant measure of center. So if you have 6+3+8+4 the numerical summary is 21. The "mean" value is 21 / 4 so 5.25 (the sum divided by however many numbers you have. Median value The second measure of central tendency is the median*. The median is the "halfway" point of a set of values; an equal number of values will fall above and below the median of a data set. Unlike the mean, the median is not overly influenced by extreme values in the data set, so we can use the median when the data is skewed. Therefore, we say that the median is a resistant measure of center. To properly find the median, values must be first sorted from smallest to largest. A union of two sets is a collection of the elements listed in both of the sets. True or False? This is a false statement. A union of two sets is a collection of all of the elements listed in the sets. C={2,4,6}C={2,4,6}D={1,3,5}D={1,3,5}The union of CC and DD is {1,2,3,4,5,6}{1,2,3,4,5,6}, as those are all of the elements that appear in the sets. The intersection* of two sets is a collection of the elements listed in both of the sets. For example: E={0,10,100}E={0,10,100}F={−2,−1,0,1,2}F={-2,-1,0,1,2}The intersection of EE and FF is {0}{0}, as 00 is the only element that appears in both sets. Empty Set--- An empty set* is a set that has no elements. There is nothing in the set; therefore, it is empty. This may seem odd, or even like it isn't a set at all, but an empty set is, in fact, a set. For example, let's say you wanted to list the days of the week that do not end in a y. There are none! Therefore, this is the empty set. In set notation, the empty set is written as a pair of brackets with nothing between them: {} subset In math and statistics, we often work with multiple sets at once. These sets can relate to one another. One such relation is known as a subset. Set AA is a subset* of set BB, if every element in AA is contained within BB. For example: A={1,2,3}A={1,2,3}B={1,2,3,4,5}B={1,2,3,4,5}AA is a subset of BB, because every element in set AA is contained within set BB. explanatory variable The variable that may be the cause of some result, or is presented as variable that offers an explanation. Also called an independent variable. Response Variable The variable that is obtained as a result, or response that gets measured or observed. Also called a dependent variable. Must know these conversions- 1Kg - 2.2lb 1000 mcg = 1 mg 1000 mg = 1 g 1000 g = 1 kg Know this conversion temperature Celsius to Fahrenheit and vice versa C = (F-32) / 1.8 F = (C x 1.8) + 32 IS in math means = OF in Math mean Multiply (x) KNOW THIS SLOPE = y=mx+B (m is rise, run) (B is y-intercept) 110 pounds - how many kilograms 110 / 2.2 (conversion rate) = 50kg Temperature in degrees Fahrenheit = Celsius x 9/5 + 32 (that is fraction 9/5)--{Can do on calculator} Temperature in degrees Celsius = (Fahrenheit - 32) x 5/9 {Can do on calculator} 16 tablespoons = 1 cup Q3 - Q1 = IQR IQR formulat **KNOW THIS What uses a 5 plot summary Box plot Median is always what in the middle Stem plot or box plot = what kind of numbers solid or whole (no 1/2 or .5) Histogram = Continuous data Stem leaf is always what less than 40 numbers Tail right = ____ skew positive Skewed date--median = middle IQR is what? Spread Mean in dot plot is always Average Mode in dot plot is always what happens most often stem plot has what type of data discrete data (solid numbers or dots) no 1/2 or .5 DOT Plot has what type of data discrete data Histogram has what type of data continuous data Two way table C - C (can be vertical or horizontal Does ____ effect _______? explanatory effect response Response is always on (top or bottom) bottom Conditional percents analyze what? two wawy tables Sid by side box plot is C - Q Scatterplot is Q - Q 5 number summary has Min, Q1, Q2(median) Q3, Max IQR Measure of spread Q3 - Q1 Closest to the river bank Scatter plot estimates Round it so it looks like money Discrete data has distinct values, can be counted, has unconnected points (think of data as dots)