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Understanding Different Types of Numbers and Data in Mathematics and Statistics, Exams of Applied Statistics

An overview of various types of numbers and data in mathematics and statistics, including integers, rational numbers, real numbers, discrete data, and continuous data. It explains the properties and characteristics of each type and provides examples. The document also covers related concepts such as sets, intervals, mean and median, and measures of spread.

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C784-Applied Healthcare Statistics 138
QUESTIONS AND ANSWERS
1. Rational number (aka Numbers that can be expressed as a fraction
'fractional')
2.
Integers Solid positive and negative numbers
3.
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.
4. True or False? Any
in-teger is also a
whole number.
5. Read all the op-tions
before answer-ing. 17-
17 is... (a. an integer b.
a rational number c. a
real num-ber d. all of
the above.)
6. set
7. Interval
This statement is false. An integer can be negative,
such as the number 100-100. 100-100 is not a
whole number.
d. all of the above. 17-17 is an integer, and all in-
tegers are also rational numbers, which in turn
are real numbers.
In mathematics, a collection of numbers is
referred to as a set*
An interval is a set of numbers between two speci-
fied values. An interval can be visualized as a seg-
ment of the number line. The segment of the
number line above that falls between 11 and 22 is
called an interval*.
8. 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 be-
tween each value.
In statistics, some data sets will be discrete. Exam-
ples 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 dis-
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C784-Applied Healthcare Statistics 138

QUESTIONS AND ANSWERS

  1. Rational number (aka Numbers that can be expressed as a fraction 'fractional')
  2. Integers Solid positive and negative numbers
  3. 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. 4. True or False? Any in-teger is also a **whole number.
  4. Read all the op-tions** before answer-ing. 17- 17 is... (a. an integer b. a rational number c. a real num-ber d. all of **the above.)
  5. set
  6. Interval** This statement is false. An integer can be negative, such as the number 100-100. 100-100 is not a whole number. d. all of the above. 17-17 is an integer, and all in- tegers are also rational numbers, which in turn are real numbers. In mathematics, a collection of numbers is referred to as a set* An interval is a set of numbers between two speci- fied values. An interval can be visualized as a seg- ment of the number line. The segment of the number line above that falls between 11 and 22 is called an interval*.
  7. 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 be- tween each value. In statistics, some data sets will be discrete. Exam- ples 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 dis-
  1. Timesheets log the Discrete. The days of the week are discrete and do days that a nurse not allow for values between them. works each week. Does the week's timesheet give data that is discrete or con-tinuous?
  2. A graph shows the Discrete. The graph shows discrete drug dosages, efficacy of a particu- not all possible dosages, between two numbers. lar drug at different dosages. Is this data discrete or continu-ous?
  3. During a physical, the nurse records the pa- tient's age, weight, and height. Are these data discrete or con- **tinuous?
  4. <
  5. d
  6. e
  7. Which of the following** is the correct transla- **tion of 3<y<4-3<y<4?
  8. How would "w is less** than or equal to 9, but greater than or equal to 5" be written?
  9. Continuous. These are all continuous measure-ments for which it is possible to have fractional parts. "less than" "greater than" less than or equal to greater than or equal to 3-3is less than y which is less than 4 (Both of the << symbols mean "less than," so the correct translation is 3-3 is less than y which is less than 4.) 9ewe5 (The answer is b. Both ee symbols mean "greater than or equal to," so 9ewe59ewe5 means "ww is less tha or equal to 99, but greater than or equal to 55.) solve the problem

In math, you may be asked to "evaluate an expression."--what does that mean?

  1. When multiplying a NEGATIVE positive number by a negative number, the product will always be
  2. Multiplying a negative Positive product (The product of two negatives will number by a negative always equal a positive.) number results in a
  3. The result of the divi- POSITIVE sion of two negative numbers is always
  4. Zero in multiplication The product* of multiplication with zero will always = equal zero; whether multiplying by a positive or a negative, any integer multiplied by zero will result in zero as the product.
  5. 8(superscript 0) Any non-zero number with an exponent of 0 (or raised to the zero power) equals 1.
  6. sampling The process of selecting research participants from a population
  7. exponent sometimes call a power, it is a number that shows how many times the baseline number is multiplied by itself
  8. probability the likelihood, or chance, that a certain event will occur
  1. 2, 3, 5, 7 are all what Prime type of numbers
  2. Prime factorization Breaking down a composite number until all of the factors are prime (like 9 is 3 and 9 )
  3. 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.
  4. Median value The second measure of central tendency is the me- dian*. 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. 40. A union of two sets is a collection of the el-ements listed in both of the sets. True **or False?
  5. The intersection* of** two sets is a collec- tion of the elements 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. For example: E={0,10,100}E={0,10,100}F={ 2, 1,0,1,2}F={-2,- 1,0,1,2} intersection of EE and FF is {0}{0}, as 00 is the only element that appears in both sets.

listed in both of the sets.

  1. 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: {}
  2. 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.
  3. explanatory variable The variable that may be the cause of some result, or is presented as variable that offers an explana- tion. Also called an independent variable.
  4. Response Variable The variable that is obtained as a result, or response that gets measured or observed. Also called a de- pendent variable.
  5. Must know these con- 1Kg - 2.2lb versions- 1000 mcg = 1 mg 1000 mg = 1 g 1000 g = 1 kg
  6. Know this conversion C = (F-32) / 1. temperature Celsius F = (C x 1.8) + 32
  1. Mode = (mode rhymes Most often (greatest frequency) with most)
  2. Median = middle Median = middle
  3. IQR FORMULA = low- Q1 - 1.5 (IQR)= outliers er limit
  4. IQR FORMULA = Up- Q3 + 1.5(IQR)= outliers per limit
  5. 1 Standard deviation = 68
  6. 2 Standard deviation = 95
  7. 3 Standard Deviation 99. =
  8. IQR = measure of spread

LEARN

  1. INEQUALITY FACES > Greater than, less than, open circle, dashed line < 0 ------
  2. e d Not greater than, Not less than, closed circle, - dashed line ________
  3. Postive slope Goes up from L&R, Like going up stairs
  4. Negative slope Goes down from L to R, Like going down stairs
  5. Slope = y (intercept {where line crosses x axis)) = mx + b (m = slope {rise/fall over run} B = Begin
  6. Histogram Single Quantative 9/
  7. Stem Plot Single Quantitative
  8. Dot Plot Single Quantitative
  9. Single Box plot Single Quantitative
  10. Pie chart Single categorical
  11. Bar Chart Single categorical
  12. Frequency is always 0 (ZERO)
  13. Skew determined by Tail
  14. Tail left = ____ skew negative
  15. Tail right = ____ skew positive
  16. Skewed date--median middle =
  17. IQR is what? Spread

Does ____ effect _______?

  1. Response is always bottom on (top or bottom)
  2. Conditional percents two wawy tables analyze what?
  3. Sid by side box plot is C - Q
  4. Scatterplot is Q - Q
  5. 5 number summary Min, Q1, Q2(median) Q3, Max has
  6. IQR Measure of spread Q3 - Q
  7. Closest to the river Scatter plot estimates Round it so it looks like money bank
  8. Discrete data has distinct values, can be counted, has unconnect-ed points (think of data as dots)
  9. Continuous data has values within a range. it is measured not count-ed, does not have gap between data points (think of data as connected lines or curves)
  10. Prime number a prime number is a number that has exactly two positive factors 1 and the number itself (2, 3, and 5 are all prime numbers)
  11. Composite numbers number that is not prime so it can be divided by another number (6, 8, 9 are all composite)
  12. Prime factorization writing the number as a product of only prime num- bers (36 = 223*3)
  1. GCF Greatest common factor--two or more numbers i the largest number that divides the given numbers evenly. (4 is the greatest common factor of 12 and
20) 
  1. Multiples of a number numbers that can be obtained by multiplying the given number by 1, 2, 3, 4 (Multiples of 3 are 3, 6, 9,15..)
  2. LCM-Least common the smallest positive number that can be divided Multiple evenly by the given number
  3. Prefix kilo = 1000
  4. prefix milli = on thousandth
  5. converg g to kg (^) g * 1kg/1000g = kg
  6. Temperature conver- Farenheit = Celsius * 9/5 + 32 sions (^) Celsius = (Fahrenheit - 32) * 5/
  7. Rise / Run y2 = y1 / x2 - x
  8. Categorical data Pie chart or bar chart (eat pie at the bar)
  9. Quantitative data Histogram, Stem plot, box plot or dot plot
  10. Stem plot is also (^) Stem and leaf plot known as what
  11. Stem plot is good for Small what type of data
  12. Box plot shows how data breaks into quarters. Each part covers 25% of the data, regardless of length. Mean is not shown on box plot
  13. Histogram good for what type of data Large data sets
  1. Dependent probability Add (Dependent is not equal)
  2. Independent probabil- Multiply (independent is equal) ity
  3. Conditional group given, of if, assume (multiply weird by given group uses words like
  4. Disjoint "or" "and" or means add and and means multiply
  5. Not Disjoint has overlap Probability (A) + Probability (B) - Prob- ability A&B (Overlap) so overlap add but subtract overlap as well 138. Dixplay x is greater than -5 using interval notation (-5, )All values greater than -5 are true for the in- equality. Greater than is denoted by a parenthesis and denotes that the value alongside it, in this ex- ample -5 is NOT to be included. The infinity symbol is always paired within a parenthesis, rather than a bracket. Therefore, (-5, ) is the interval notation