AP Stats Extravaganza

science of data, information gathered into useful figures

one singular object described by a set of data

any characteristics measured or collected in a data set

places an individual into a category or group

measures a specific numerical value that can be used for analysis

the frequency distributions of values of cat. variables among all individuals in a two-way table

gives the frequency distribution of a specified group

relationship between two variables, value of one variable occurs in combination with values from another variable

shape, outliers, center, spread

graph's shape, whether it's symmetric or skewed left/right

any unusual data that doesn't fit, Q1-1.5IQR and Q3 +1.5IQR

described by mean or median, use median unless the data is symmetric

variability in data, range & standard deviation

one mode

two modes

multiple modes

no distinct mode

how much a measure is influenced by extreme values, median is resistant, mean, s.d. and range are not

minimum, first quartile, median, third quartile, maximum

average distance of a value from the mean

average squared distance from the mean

data skewed to the right have the "tail" of the data on the right and vice versa

how many standard deviations you are away from the mean

the nth percentile is the lowest score that is greater than a certain percentage

changes the mean but not the standard deviation or range

changes range, mean, median, standard deviation

median, mean, quartiles, percentiles

standard deviation, range

a curve on or above the horizontal axis, total area underneath is equal to one, 100% of observations

shown by a normal density curve with the mean, median, and mode at the center of the curve

68% of values within one standard deviation of the mean, 95% within two, 99.7% within three

N(u, o) a.k.a. (mean, standard deviation)

a table of areas under the standard normal curve, table entry for each value of z is the area under the curve to the left of the z-score

when n is large, the sampling distribution of the sample mean is approximately normal, n is greater than or equal to 30

quantitative data that has two variables, often represented w/ a scatterplot

independent variable, used to explain or to predict changes in values of another variable

dependent variable, measures the outcome in response to the explanatory variable

if a graph has a negative/positive "slope", ranges from -1 to 1, r-value

direction, outliers, form, strength - all things that should be addressed when describing the relationship between two quantitative variables on a scatterplot

a line describing how the response variable changes as the explanatory variable changes

the line that makes the sum of the squared residuals as small as possible

a pitfall of statistical prediction, use of a regression line to predict values outside the data interval

the difference between the observed value of the response variable and the value predicted by the regression, outliers have a large residual

any point that, if removed, changes the relationship/regression significantly, a regression will change up or down if you remove/replace influential points

least squares regression line

a graph showing the residuals on the vertical axis and the explanatory variable on the horizontal axis, you want it to be random to show a linear relationship

r^2, tells what percent of the variation in data values is explained by the regression line

preserve linear relationship, e.g. addition, subtraction, multiplication, division

don't preserve linear relationship, e.g. roots, exponents, logarithms

to increase linear relationship

• conduct standard regression

• construct residual plot and transform it if the plot has a pattern

• evaluate r^2

• choose transformation method

• transform one or both variables

• conduct another regression analysis

• find the new r^2 and it should be higher than the original r^2

the entire collection of objects or individuals about which information is desired

a subset of the population being studied

a survey that collects information from every member of a population

observe and measure variables

manipulate variables & see results

statistical data from a sample that are used to draw conclusions about the entire population

define the population, tell what the researcher wants to measure, show how data members of a sample set are chosen, represent the population accurately in the sample, are free from bias

biased design, convenience sample, voluntary response, undercoverage, nonresponse, response bias

over/under estimating the desired response in a survey consistently, similar to accuracy

choosing only individuals for a survey who are easy to access

when sample members are allowed to volunteer

when members of the population are represented inadequately in a sample

when the individual selected for the sample is left out or refuses to participate

a group or set chosen to replicate characteristics of a larger population

a group or set chosen in a random manner that allows for each member of the population to have an equal chance at being selected

simple random sample, every individual has the same chance of being selected and every possible sample has the same chance of being selected

divide population into subgroups called strata then conduct SRS from each subgroup

form of SRS, first person is random & the rest are chosen systematically

select clusters randomly from population, selecting groups randomly, not individuals from groups

observe responses to variables, administer a treatment to observe response, attempt to determine causation

only observe responses, don't attempt to influence responses

replication, randomization, control

assigning treatment to many experimental units to lower variability

using chance to assign groups, use a random number tables/number generators

control for confounding variables or outside influences

not telling subjects or researcher what treatments subjects are receiving to eliminate bias

analyzes data from a subset of a population, can be costly & time-consuming

analyzes data from a certain point in time, focused type of sample survey

method of dividing subjects into subgroups called blocks so the variability in blocks is less than the variability between blocks, controls for variables you know (randomization controls for variables you don't know)

experimental method where subjects are grouped into pairs based on a blocking variable, one is control and one is treatment

variables other than independent/dependent variables that may affect experimental outcomes

a subject's positive response to receiving a placebo when no treatment has actually been applied

variables that affect the response variable under consideration

cause and effect relationship between or among variables, experiments can determine causation

participants must give informed consent, data collected must be private if it's personal info, risks to participants must be minimized

a paradox in statistics in which a trend appears in different groups of data but is reversed when those groups are combined

the likelihood that an event will occur, the mathematics of chance

as we observe more and more repetitions of any chance process, the proportion of times a specific outcome occurs approaches a single value

probability in actual trials

probability calculated with a formula, not based on observed sample

when the occurrence of one event does not change the probability that the other event will happen

• always between zero and 1

• sum of possible outcomes of a trial must equal 1

• complement rule: the probability of an event occurring is one minus the probability that it doesn't occur

any outcome or collection of outcomes that is a subset of the sample space

raise the number of outcomes in one trail to the power of the total number of trials

a random process of numerous trails used to estimate probability and imitate chance behavior

• state the problem

• state the assumptions

• describe the process for one repetition, including possible outcomes, assigned representations, & measured variables

• simulate many repetitions

• state conclusions

the probability that the event won't occur

two events have no outcomes in common

the probability of an event given another event has occurred