AMS 110 Exam 1 Terms

variable

quantity that is observed in an experiment

sample space

set of all possible outcomes (can be finite or infinite)

discreet sample space

finite number of elements (or countably infinite)

continuous sample space

infinite number of elements (not countable)

ex: 2 < x < 5

independent event

the occurrence or non-occurrence of one event does not change the probability of the other event's occurrence

ex: drawing cards with replacement

dependent event

the occurrence or non-occurrence of one event does change the probability of the other event's occurrence

ex: drawing cards without replacement

mutually exclusive

(disjoint)

two events do not intersect / do not occur at the same time

always dependent

collectively exhaustive

includes all possible outcomes

partition

events are said to _______ a sample space S if they are mutually exclusive and collectively exhaustive

sensitivity

probability that a test shows positive, given that the patient has the disease

specificity

probability that a test shows negative, given that the patient does not have the disease

descriptive statistics

the act of describing, organizing, and summarizing data (using tables, plots, charts, etc.)

statistics

the collection, analysis and interpretation of data

bar graph

graph used for categorical (qualitative) data (bars do not touch, separated by categories)

histogram

graph used for quantitative data (bars touch)

scatter plot

graph used to show patterns in data, may include line of regression

line of regression

line of best fit, used to show a linear relationship in a scatter plot

stem and leaf plot

plot used to order data by number places

frequency polygon

histogram with the midpoints connected to show progress in data (great for comparisons)

circle graph

graph that shows categories (qualitative data) as parts of a whole

grouped frequency table

table that groups quantitative data into classes (used for histograms)

inferential statistics

uses sample statistics to draw conclusions (inferences) about population parameters

parameter

a number that describes some characteristic of a population (μ, N, σ)

statistic

a number that describes some characteristic of a sample (x̄, n, S)

simple random sampling

each member of the population has the same chance of being selected for the sample

(every possible sample of size n has the same chance to represent the entire population of size N)

random number table

table used to choose a random sample (n) from a population (N)

stratified random sampling

members of the population are divided into two or more homogenous subsets (strata) that share a similar characteristic, a random sample is then taken from each stratum

proportionate allocation

we may select a number from each stratum that is proportional to the breakdown of these groups (ratio)

stratified random sampling

ensures each segment of the population is represented

differences within groups = small

differences between groups = bigger

disproportionate allocation

(optimum allocation)

used if larger samples are taken in the strata with greatest variability to capture the variability

1 in k systematic sampling

each member of the population is assigned a number

a starting number is randomly selected from amongst the first k members, then every kth member is selected from the starting number (i.e. every 3rd, k = 3)

probability sampling

every member of a population has an equal chance of being selected to the sample (best for representing whole population)

cluster sampling

divide the population into mini-populations (clusters), then randomly select a few of them, include all members of the cluster in your sample

differences within clusters are large

differences between clusters are small

can obtain a bigger sample with this method

non-probability sampling

not every member of a population has an equal chance of being selected to the sample

(ex: convenience sampling, voluntary response)

contains bias and unreliable data

qualitative random variable

variable that places an individual into one of a group of categories (cannot be measured)

sex

eye color

hair color

race

etc.

nominal data

qualitative data with names only

sex

states

continents

yes or no

ordinal data

qualitative data that can be ordered/ranked

bed sizes

degrees of burns

stages of disease

days of week

quantitative random variable

variable that takes on a numerical value that is measurable

interval data

quantitative data with no start point or "0" value

clock times

calendar years

temperature (°C or °F)

ratio data

quantitative data with a start point or "0" value

time lapses

age

pressure

temperature (Kelvin)

length

mass

independent variable

(x) variable that is manipulated in an experiment

dependent variable

(y) variable that is influenced by independent variable

correlation

describes the strength and direction of the linear relationship between 2 quantitative variables (has no units)

(the closer to 1 the correlation coefficient is, the stronger the linear relationship)

dichotomous variable

type of variable that only has two values

sex (male or female)

coin-flip (heads or tails)

exam result (pass or fail)

variance

standard deviation squared

measure of the variability (scatter) of values from the mean of a data set

standard deviation

square root of variance

measure of the variability (scatter) of values from the mean of a data set

low = values clustered close to mean

high = values spread farther from mean

sample standard deviation

square root of the sample variance

better to use in the presence of outliers, since standard deviation is thrown off by them

adding/subtracting

______/___________ a constant from xi changes the mean, but not the standard deviation, variance, or range

it only shifts data to the right (+c) or left (-c)

multiplying

___________ a constant by xi changes the mean, standard deviation, variance, and range

coefficient of variation

a way to interpret the relative magnitude of the standard deviation

useful for comparing two dispersions of two variables

higher percent CV = more variable data

the empirical rule

for mound-shaped distributions only

gives the approximate percentage of measurements that fall within 1, 2 and 3 standard deviations from the mean (applies to populations or samples)

68-95-99.7% rule

z score

represents the distance between the measurement and the mean, expressed in standard deviations

(tells you how many standard deviations a given value (x) is above or below the mean)

positive = above mean

negative = below mean

Chebyshev's Theorem

for any set of data and for any constant (k), while k > 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least 1 - (1/k²)

k = number of standard deviations from the mean