Terms Flashcards
Whole Numbers
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.
Integers
A number (positive, negative, or zero) that can be represented without a fractional or a decimal component.
rational number
Any number that can be represented as a fraction of two integers. Equivalently, any number which has a decimal that either terminates or repeats.
real numbers
Any numbers on the number line. Real numbers include zero, negative and positive integers, rational numbers, and even numbers that are not rational (such as π).
set
In Mathematics: a set is a collection of things, usually numbers. You’ll see some sets that aren’t numbers later in the text.
Discrete data
A collection of numbers whose values are distinct, separate, and unconnected.
Continuous
A collection of numbers whose values are not divisible into distinct units.
interval
A set of numbers between two specified values.
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.
additive inverse
Two numbers equidistant from 0 on a number line whose sum is 0. 3 and -3 are additive inverses.
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.
factor
An integer that evenly divides a larger number
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.
PEMDAS
prime factorization
Determining the set of prime numbers whose product is the original integer.
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.
square root
A number that produces a specified number when it is multiplied by itself.
principal square root
negative square root
The positive square root of a perfect square. For example, the principal square root of 36 is 6.
The negative number that equals the given number when squared. For example, -6 is the negative square root of 36.
radical sign
radicand
The sign √ which indicates the square root of the number that follows.
The number under or after the radical sign √ which is having its square root taken. The radicand of √ 4 is 4.
Equivalent fractions
Different fractions that represent the same value
least common multiple (LCM)
The smallest number in value that is a multiple of two or more numbers.
repeating decimal
terminal decimal
A decimal number that has either a digit, or sequence of digits, that repeat forever. A bar written over the top of the part of the decimal that repeats.
A decimal number that has a finite number of digits.
Equations for Temperature Conversion
To convert to Fahrenheit:
Temperature in degrees Fahrenheit=Celsius×9/5+32
To convert to Celsius:
Temperature in degrees Celsius=(Fahrenheit−32)×5/9
variable
A symbol that represents a mathematical value.
coefficient
A number by which a variable is being multiplied.
inverse operations
Two operations that undo one another.
like terms
Terms that have the same variable(s) with the same exponent(s). These terms can be “combined” using addition or subtraction.
degree
the largest exponent in an expression
coordinate plane
A tool used for graphing that is a display of a two dimensional plane. It consists of an x-axis and a y-axis; the x-axis being a horizontal number line, the y-axis is a vertical number line, and the axes meet at the origin (0,0).
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.
Two Types of Data
Quantitative data, also called numerical data, consists of data values that are numerical, representing quantities that can be counted or measured.
Categorical data, also called qualitative data, consists of data that are groups, such as names or labels, and are not necessarily numerical.
Histograms vs. Bar Charts
Histogram: displays frequencies or relative frequencies for quantitative data
Bar Chart: displays frequencies (i.e., counts) or relative frequencies for categorical data
symmetry
skewed distribution
The quality of the data having the same shape on both sides of the mean
A distribution that is not symmetrical but has a greater quantity of data on one side.
reliable data
valid data
Data is both consistent and repeatable.
Data that results from a test that accurately measures what it was intended to measure.
bimodal
multimodal
A description of a data set that has two peaks, or modes.
A description of a data set that has two or more peaks (modes).
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
Mean
Median
mode
Average, calculated by adding a series of elements in a data set together and dividing by the total number in the series.
The value or quantity lying at the midpoint of a frequency distribution.
The most frequent value in a dataset.
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.
Range
interquartile range
The difference between the minimum and maximum value in a given measurable set
The difference, in value, between the bottom and top 25 percent of the sample or population
outlier
1.5 IQR Criterion Rule
An observation point (number) that is significantly distant from the other observations in the dataset.
Outliers are defined to be any points that are more than 1.5 × IQR above Q3 or below Q1
five-number summary
The minimum, first quartile, median, third quartile, and maximum. A box plot represents the five numbers in a five-number summary.
standard deviation
Standard Deviation Rule
The measure on average of how far the data points are from the mean.
A standard proportion or percentage of data points that lie within each standard deviation away from the mean for a normal distribution.
Approximately 68% of all values are within 1 standard deviation of the mean
Approximately 95% of all values are within 2 standard deviations of the mean
Approximately 99.7% of all values are within 3 standard deviations of the mean
explanatory variable (independent variable)
response variable (dependent 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.
The variable that is obtained as a result, or the response that gets measured or observed. Also called a dependent variable.
joint frequencies
marginal frequencies
The frequency counts in the interior cells, or the ones that form an intersection between two variables.
The totals of each row and column in a table; given this name because they are in the ‘margins’ of the table
correlation
An observed relationship between two quantitative variables. While this is most commonly a linear relationship, it does not need to be. Note that observing a relationship does NOT imply that there is a meaningful causal link between the variables.
positive correlation
negative correlation
When two quantitative variables move in the same direction; the response variable increases when the explanatory variable increases.
When two quantitative variables move in opposite directions: as the explanatory variable increases the response variable decreases.
correlation coefficient
A measure of the linear relationship between two attributes. Correlation coefficient is denoted by r. The numerical value demonstrates how closely the attributes vary together. Correlation coefficients near -1 and +1 have strong linear correlation, while a correlation coefficient near 0 has weak (or no) linear correlation.
non-linear
An expression or equation that is illustrated by something other than a straight line
cluster
Several points are grouped together away from the majority of points in a data set
observational study
experimental study
The researcher observes if there is an association between variables. There is no treatment or control group.
The researcher applies a treatment to one group and no treatment (or placebo) to a control group, to determine if there is causation between variables.
Voluntary Sample
Stratified Sample
Cluster Sample
Researchers invite everyone in the sampling frame to participate. Individuals who voluntarily respond comprise the study sample.
Researchers break up the population into separate and distinct categories and some people are selected from each category to obtain the study sample.
Similar to stratified sample the population is broken into categories and all people from some of the categories are selected obtain the study sample.
Causation
causal relationship
The relationship of cause and effect.
A relationship between two variables that can be classified as cause-and-effect.
lurking variable
A variable that is not included in an analysis but that is related to two (or more) other associated variables which were analyzed.
Simpson’s Paradox
A counterintuitive situation in which a trend in different groups of data disappears or reverses when the groups are combined.
Regression Analysis
A statistical analysis tool that quantifies the relationship between a response variable and one or more explanatory variables.
linear interpolation
linear extrapolation
Estimation using the linear regression equation is between known data points.
Estimation using the linear regression equation is made outside known data points.
least squares
A technique for finding the regression line.
hypothesis test
A statistical test that tell us whether a result is significant
p-value
The probability that a result was caused by chance
significance level
The p-value cutoff for statistical significance. Any p-value below the set significance level is considered statistically significant.
subset
Set A is a subset of set B, if every element in A is contained within B.
union
The union of A and B will have all elements in A, all elements in B, and all elements in both. You can think of a union as “A or B,” since it contains an element if it is in A or in B. The union of many sets will have an element if it appears in at least one set.
intersection
The intersection of A and B will have all elements that are in both A and B. In other words, intersection defines the set of elements which are in both sets. The intersection of many sets will have an element if it appears in all of the sets.
theoretical probability
Also called the “Actual,” “Exact,” or “Classical” Probability, it is computed by dividing the number of outcomes where the desired event occurs by the total number of outcomes. Note that the outcomes must be equally likely.
empirical probability
relative frequency
A probability that is calculated by conducting trials or experiments and recording the results.
A way to approximate a percentage by dividing the number of times an event occurred in an experiment by the total number of trials.
law of large numbers
A law in probability that as the number of experiments gets larger, the relative frequency of an outcome will converge on the theoretical probability.
converge
when values (such as empirical probabilities) get closer and closer to a particular value (like the estimated probability of an event happening).
sample space
sample size
The set of possible outcomes for an experiment
In statistics, sample size refers to the number of individuals measured or observed in a study. In probability, sample size refers to the number of possible outcomes in a trial or experiment.
complement
The occurrence of an event not happening, the opposite.
disjoint
Two events that cannot occur at the same time.
addition rule of probability
For disjoint events A and B, P(A or B) = P(A) + P(B)
independent events
Events, where the occurrence of one does not affect the probability that the other event(s) will occur.
multiplication rule for independent events
If two events are independent P(A and B) = P(A) × P(B).
Conditional Probability Rule
General Addition Rule
Determining Independence
law of total probability
A fundamental mathematical principle that states that the sum of the product of all sequences of possible outcomes in a sample space is 1. In a probability tree, first multiply each branch of the tree, then sum the products to get 1.
