aka Bar chart

Illustrates the distribution of categorical variables, which are usually placed on the x-axis, and percent relative frequency on the y-axis. Includes Pareto diagrams.

aka Bernoulli distribution.

When there are two possible outcomes or a probability experiment: success and failure.

You have to use the nCr function on your calculator, simbolized by C.

P(X = x) = (n C x)p^x(1 - p)^n-x

aka Qualitative variable

A variable that falls into one of two or more distinct categories. May be displayed using a bar graph, Pareto diagram, or pie chart.

aka Chebyshev's theorem

The proportion of observations that lie within k standard deviations must be at least 1 - (1/k²)

aka Bins

Ranges of quantitative variables that data is sorted into when making a frequency table. Appropriate number and range of bins must be selected, with boundaries the same for each class.

A permutation where the order of selection doesn't matter.

x is the number of items in the combination

n is the number of items x is selected from

Cⁿ_x = [n!] / [x!(n - x)!]

^C

An event has not occured.

P(A^C) = 1 - P(A)

|

An event that has occured given that another event has already occured.

P(A|B) is the probability of A, given that B has already occured.

A sliding continuum of values. There are infinity number of fractions it can be divided into. May be bound to a certain range.

Example: time, weight, distance.

The theoretical value of a mean variable. Not to be confused with the most likely value. The average if an experiment was done infinity times.

μ = E(x) = Σ x p(x)

A population which is small enough for every member to be listed.

Example: U of G students.

aka 25th percentile

The bottom section of the box in a boxplot. Included in the five-number summary.

A measure of central tendency. The nth root of the product of observations.

(Πxi)^(1/n)

A measure of central tendency. The reciprocal of the mean, using reciprocals of all observations.

n / [∑(1 / x_i)]

Binomial distribution where the trials are not independent; the probability of outcomes is dependent on the results of previous trials.

You need to use the nCr function on a calcultor, symbolized by C.

X is the number of successes

a is the probability of a success

n is the sample size

N is the population size

P(X = x) = [(a C n)*((N - a) C (n - x))] / [N C n]

The occurance of an event has no effect on the probability of an another effect and vise versa.

All three must be true or all three false:

1. P(A∩B) = P(A)*P(B)

2. P(A|B) = P(A)

3. P(B|A) = P(B)

aka Unit

aka Case

Objects on which measurements are taken.

A descriptive measure of variance. The difference between the third and first quartile. Not sensitive to extreme values.

IQR = Q₃ - Q₁

∩

One event and another event have occured together in the same sample point.

aka Average

The most popular measure of central tendency. Uses more information, but is more sensitive to extreme values in the data. This sensitivity can make the mean misleding

x bar = [Σx_i] / n

The average absolute value of deviation. A reasonable measure of variability, but hard to work with.

MAD = [Σ|x_i - x bar|] / n

aka Second quartile

aka 50th percintile

A measure of central tendency. The line in a boxplot separating the box. The middle point, if all data points were ordered in ascending order. If n is even, the median is the  average ot the two middle values. Not as sensitive to extreme values as the mean. Good for data that is right-skewed, such as property value or salary.

Evens where there is no outcome in the sample space that satisfies both.

P(A∩B) = 0

Researchers observe and measure variables, but do not impose any conditions on the subjects. The groups of explanatory variables are pre-existing. 

Done if the experiments are impossible (time, money, ethical reasons). Doesn't provide strong evidence for causal relationships; there may be lurking variables.

An ordering of a set of items. 

x is the number of things being ordered

n is the number of things x is selected from 

Pⁿ_x = [n!] / [(n - x)!]

When events occur independently over a range. The probability of an event within any given range of a certain size does not change. 

X is the number of events in a fixed range

 x is a positive integer

λ is the theoretical mean of events in a fixed range

P(X = x) = [λ^xe^-λ] / [x!]

Used to calibrate the probability a success will occur after a certain number of trials.

P(X = x) = p*(1 - p)^{x - 1}

P(X ≤ x) = 1 - (1 -p)^x

A measure of variability. The average squared deviation. Will give an answer in units squared.

s² = [Σ(xi - x bar)²] / (n - 1)

The squared root of variance. Cannot be negative.

s = √s²

aka Stem-and-leaf display

A way of illustrating quantified variable data. The data is sorted into stems and leaves based on the last two digits. The leaves are listed as single digits (the last digit in the data point) to the right of their stem. Must include a legend for the stems. Includes split-stem and back-to-back stemplots.

aka Bell-shaped distribution

Distribution that is roughly the same on either side of the median. Includes normal distribution.

aka 75th percentile

The top line of a boxplot.

U

One event or another event has occured in one sample point.

The dispersion of a variable.

Var(x) = E * [(x - μ)²] = E * (x - μ)² * p * x

A unitless measure of how many standard deviations a point is away from the mean. Positive means above the mean, negative means below.

z_i = [x_i - x bar] / s