Applied Probability and Statistics – C955 Flashcards
continuous
A collection of numbers whose values are not dividable into distinct units.
subtraction
Taking one or more values away from another.
associative property
The associative property holds that under certain operations in a multi-step expression, the computations may be done in any order. Commonly represented as (a + b) + c = a + (b + c). Addition and multiplication are associative.
composite number
A number with more factors than just one and itself.
principal square root
The positive square root of a number. For example, the principal square root of 36 is 6.
negative number
A number whose value is less than zero. On the number line, negative numbers are to the left of zero.
multi-step expression
An expression or equation with more than two values and two or more operators that requires multiple steps to be solved.
prime number
A number with only two factors: one and itself
multiplication
In mathematics, multiplication is the act of adding the same number multiple times. Multiplication is often denoted by the dot sign,
operation
In mathematics, an operation is a procedure which generates a new value from one or more operands, or mathematical values.
product
The result of multiplying values.
division
Splitting values into equal parts or groups
multiplicative inverse
The multiplicative inverse of a number x is the number you must multiply x by to get 1. For example, 5 and 1/5 are multiplicative inverses.
exponents
Sometimes called a power, it is a quantity that represents repeated multiplication
numbers
A word or symbol (such as ‘five’ or ‘16’) that represents a specific amount or quantity.
expressions
A string of terms that are connected by division, addition, and subtraction operations.
radicand
The number within the radical sign whose square root is to be taken.
data
A set of values of qualitative or quantitative variables; pieces of data are individual pieces of information.
base number
The number multiplied by itself when paired with an exponent. For example, in 8 to the third power, 8 would be the base number.
operators
A word or symbol (such as + or -) that indicates an operation between values.
whole number
A number whose value is 0 or greater (negative numbers are not considered whole numbers) and can be represented without a fractional or a decimal component.
addition
Finding the total of two or more values.
factor tree
A graphical method used to identify the prime factorization of an integer.
estimation
Approximating a value for a calculation
identity property
The property that 0 can be added to any number without changing the value of the number. Likewise, 1 can be multiplied by any number without changing the value of that number.
set
In mathematics: a collection of numbers.
radical sign
The symbol which indicates to take the square root of the number that follows.
Fundamental Theorem of Arithmetic
A concept which states that any integer greater than 1 is either prime or is the product of a unique set of prime numbers.
quotient
The result of a division expression.
parentheses
In mathematics, parentheses () are used to separate operations within an expression. Any operations that lie within parentheses should be performed first.
negative square root
The negative square root of a perfect square. For example, -6 is the negative square root of 36.
superscript
A symbol (such as a number or letter) written above and immediately to the left or right of another character.
interval
A set of numbers between two specified values
commutative
The property that the order of the numbers under the operation does not change the result. Addition and multiplication are commutative: a + b = b + a and ab = ba.
greatest common factor (GCF)
The greatest common factor of any two integers a and b is the greatest number that is both a factor of a and a factor of b
rational number
A rational number is a number that can be written as a ratio of integers, which means it can be written as a fraction.
integer
A number, (positive, negative, or zero), that can be represented without a fractional or a decimal component.
additive inverse
Two numbers equidistant from 0 on a number line whose sum is 0. For example, 3 and -3 are additive inverses
real number
Any numbers on the number line. Real numbers include zero, negative and positive integers, fractions, and decimals.
sum
The result of multiple numbers being added together.
order of operations
A set of rules that defines the order in which mathematical operations should be performed
perfect square
The product of any integer with itself yields a perfect square. So, a number is a perfect square if it can be written as the square of an integer. For example, 9 is a perfect square because 3 * 3 = 9.
factor
An integer that divides another integer. We say an integer, x, is a factor of another integer, y, if the quotient y/x is also equal to an integer.
difference
The result of one number being subtracted from another number.
discrete
A collection of numbers whose values are distinct, separate, and unconnected
square root
A number that produces a specified number when it is multiplied by itself.
prime factorization
Determining the set of prime numbers whose product is the original integer.
positive number
A number whose value is greater than zero. On the number line, positive numbers are to the right of zero.
factorization
The process of determining the prime factors of a composite number.
percent proportion
Proportion that is equivalent to the given ratio but has a denominator of 100. So the Percent Proportion of 3/5 is 60/100.
numerator
The number that is written before the slash, or above the fraction bar, in a fraction.
proportion
A true statement in which two ratios are equal to each other.
unit cancellation
The act of a unit being crossed out when the unit is in a numerator, and the same unit is in the denominator of a fraction or a product of fractions.
conditional proportion
A proportion where one part of a proportion is a variable, or unknown quantity.
ratio
Measures one quantity in relation to another quantity.
cross products
The results produced from cross multiplication.
denominator
The number written after the slash, or below the fraction bar, in a fraction.
reciprocal
A reciprocal of a number is that number which, when multiplied by the original number, equals 1. It is the same as the multiplicative inverse.
least common multiple (LCM)
The smallest number in value that is a multiple of two or more numbers.
unit multiplier
A fraction that contains two equivalent quantities but in two different units, used in order to convert units.
multiple
A multiple of an integer is that integer multiplied by another integer. For example, 28 is a multiple of 7 because 28 = 7*4.
repeating decimal
A decimal number that has either a digit, or sequence of digits, that repeat forever. A bar is written over the top of the part of the decimal that repeats.
rounding
A method of estimating in order to make working with a number easier.
fractions
The representation of a number as a division of one integer by another through the use of a slash or division bar
butterfly method
Cross-multiplication method used to determine whether two fractions are equal. The numerator of one fraction is multiplied by the denominator of the opposite fraction on both sides.
rate
A ratio that compares two quantities having different units of measure.
percent sign
A symbol used to denote percentages.
equivalent fractions
Different fractions that represent the same value.
place value
Describes what part of the whole the decimal represents.
terminal decimal
A decimal number that has a finite number of digits.
cross multiplying
A method used to prove that a proportion is true
improper fraction
A fraction where the the number in the numerator is more than the number in the denominator.
trailing zeros
Sequence of zeros after the last non-zero digit in a decimal number.
unit conversion
A method used to change between measurement systems.
proper fraction
A fraction where the number in the numerator is less than the number in the denominator.
percentages
Like fractions, they denote something that is not necessarily whole, but rather could be a part of a whole number. 100% represents the number one.
exponent
Sometimes called a power, it is a quantity that represents repeated multiplication.
degree
The largest exponent in an expression.
addition principle of equality
The fact that we can add the same number to both sides of an equation, and the result will be an equivalent equation.
elementary operation
Addition, subtraction, multiplication, and division.
vertical line
A line that runs up and down on the coordinate plane, parallel to the y-axis. It has no ‘run’ or change in x-value.
algebraic equation
Any equation that contains variables, constants, or mathematical operations.
x-axis
The horizontal line that passes through the origin on a coordinate plane.
quadratic
An expression or equation of degree 2.
slope-intercept form
A common format that a linear equation can take that is helpful for graphing purposes. It is of the form y = mx + b, where m is the slope of the line and b is the y-intercept.
arithmetic expression
A string of numbers connected by elementary operations.
constant
A value that is known and unchanging.
division principle of equality
If both sides of an equation are divided by the same number, the result is an equivalent equation.
the principle of equality
If you perform equivalent operations to both side of an equation, the result will always be an equivalent equation.
ordered pairs
Two numbers written in the form (x, y), where x represent the x-value or x-coordinate, and y represents the y-value or y-coordinate.
cubic
An expression or equation of degree 3.
variable
A symbol that represents a mathematical value.
term
An individual number, a variable, or numbers and variables multiplied together. They are separated by addition, +, or subtraction, -, in an expression.
combining like terms
Combining terms that have the same variable component. Combining like terms helps to consolidate when solving an equation.
equation
Two mathematical expressions separated by the equals sign, =. The two expressions on either side of the equals sign hold the same value as one another.
multiplication principle of equality
If both sides of an equation are multiplied by the same number, the result is an equivalent equation.
y-intercept
The y-value of the point at which a line intersects with the y-axis.
subtraction principle of equality
The fact that we can subtract the same number to both sides of an equation, and the result will be an equivalent equation
distributive property
A mathematical principle used to multiply one term by multiple terms. This principle is employed when there are parentheses around multiple terms, which are in turn multiplied by a single term.
coefficients
A number by which a variable is multiplied. This number is written in front of the variable(s).
linear
An expression or equation of degree 1.
y-axis
The vertical line that passes through the origin on a coordinate plane.
unlike terms
Terms that do not have the same variable(s) with the same exponent(s). These terms can not be combined using addition or subtraction.
value
A number or numerical worth.
horizontal line
A line that runs left to right on the coordinate plane, parallel to the x-axis. It has no ‘rise’ or change in y-value.
Order of Operations
A set of rules that defines the order in which mathematical operations should be performed.
operation
A procedure which generates a new value from one or more operands, or mathematical values.
quadrants
The four sections of the coordinate plane, separated and defined by the x-axis and y-axis.
The Butterfly Method
Cross-multiplication method. The numerator of one fraction is multiplied by the denominator of the opposite fraction on both sides.
like terms
Terms that have the same variable(s) with the same exponent(s). These terms can be ‘combined’ using addition or subtraction.
inverse operations
Two operations that undo one another.
slope
The value that describes the direction and steepness of a line drawn on the coordinate plane. It is measured by ‘rise over run.’ Rise/Run = (the change in y value) / (the change in x value) = (y2 - y1)/(x2 -x1)
origin
The point (0,0) on a coordinate plane, which is where the x-axis and y-axis intersect.
algebraic expression
A string of terms that are connected by division, addition, and subtraction operations.
the substitution method
When a variable is substituted by its known value in an algebraic expression or equation.
data
A set of values of qualitative or quantitative variables; pieces of data are individual pieces of information.
standard deviation
The measure on average of how far the data points are from the mean.
center
One of three measures that describe what is “normal” in a data set: mean, median, or mode.
the Standard Deviation Rule
A standard proportion or percentage of data points that lie within each standard deviation away from the mean for a normal distribution.
measure of central tendency
A summary measure that is used to describe an entire set of data with one value that represents the middle or center of the data set’s distribution. There are three main measures: mean, median, or mode.
normal distribution
A common type of distribution of data points that forms a bell shaped, symmetrical curve around the mean
maximum
The largest value in a set.
qualitative data
Non-numeric information based on some quality or characteristic.
reliable data
Data is both consistent and repeatable.
histogram
A graph that displays data through vertical bars that show the counts or numbers in each range.
graphical displays
Visual displays of data sets.
stem plot
A visual representation of data in which individual data points are plotted to the right of a vertical line, or chart, and the left (the “stem”) shows the interval categories.
outlier
An observation point that is significantly distant from the other observations in the dataset.
numerical summary
A number used to describe a specific characteristic about a data set.
quartile
Values that divide a data set into four equally sized groups.
multimodal
A description of a data set that has more than two modes.
minimum
The smallest value in a set.
skewed left
A skewed distribution where the long tail of the curve is on the negative side of the peak.
valid data
Data that results from a test that accurately measures what it was intended to measure.
measures of spread
A number of measures used to determine the distance of data from the center of the data set, such as range and standard deviation.
dot plot
A graphical representation of data that plots the frequency of data along a horizontal line.
distribution
An arrangement of values that illustrates their frequency or occurrence.
data set
Any collection of numerical values, such as measurements, observations, or survey responses.
skewed right
A skewed distribution where the long tail of the curve is on the positive side of the peak.
statistics
The science that deals with the interpretation of numerical facts or data through theories of probability. Also, the numerical facts or data themselves.
mean
Average, calculated by adding a series of elements in a data set together and dividing by the total number in the series
unimodal
A set of data having one mode.
bimodal
A description of a data set with two modes
categorical data
This type of data, also called qualitative data, consists of data values that can be sorted into groups or categories.
skewness
A measure of the degree to which a probability distribution “leans” toward one side of the average, where the median and mean are not the same.
five-number summary
The minimum, first quartile, median, third quartile, and maximum. A box plot represents the five numbers in a five-number summary.
shape
The outline of a set of data displayed on the coordinate axes.
median
The value or quantity lying at the midpoint of a frequency distribution.
quantitative data
Data values that are numbers, representing quantities that can be counted or measured.
symmetry
The quality of the data having the same shape on both sides of the mean.
pie chart
A graphical display that shows data in categories as percentages of a circle.
range
The difference between the maximum and minimum values.
box plots
A graphical rendering of the range and the first and third quartiles of a data set with the data set’s median in between.
check sheet
A structured form or table that allows data to be collected by marking how often an event has occurred in a certain interval.
mode
The most frequent value in a dataset.
frequency distribution
A record of the number of times data occurs within a certain category.
skewed distribution
A distribution that is not symmetrical but has a greater quantity of data on one side of the mean.
scale
The relationship between units and their visual representation on a graph.
bar chart
A graph that displays data that is distributed over groups or categories.
interquartile range
The difference, in value, between the bottom and top 25 percent of the sample or population.
