Intro to Business and Economic Statistics

population

a collection of individuals or objects that is under study

sample

a subset of the population

variable

a characteristic of interest about each individual element of a population or sample

data

numbers or information with a context

different characteristics are measured for different individuals in the population or in the sample

quantitative data

variables that can assume numerical values

qualitative data

variables that are not numerical

observations are categorized into various groups or categories

data collection

obtained from...a published source, designed experiment, survey, observational study

sampling

-representative of the population

-have characteristics typical of the target poulation

simple random sample

sample in which each element in the population has an equal change of being selected

systematic sample

sample in which the first element is picked at random, and then every kth element is picked

-there should be an ordering among the elements for us to use this

stratified random sample

sample obtained by stratifying the sampling frame and then selecting a fixed number of elements from each strata by simple random sampling

cluster sample

sample obtained by sampling some of, but not all of, the possible subdivisions within the population

frequency distribution

tabular summary of data showing different classes and the frequency (or number) of items in each of several non-overlapping classes

shows how the observations in the sample are distributed

objective is to provide insights about the data that cannot be quickly obtained by looking only at the original data

relative frequency

total number of observations belonging to the class

distribution

describes how the observations are spread over the range of the data

Symmetric distribution

mount shaped

Negatively skewed/skewed to the left

positively skewed/skewed to the right

center

measure of the central tendency

variability

spread of the data

mean

average of a group of numbers

mode

most frequent observation

median

most middle observation

range

maximum - minimum

variance

tells us the squared distance between a typical observation and the mean of the data

standard deviation

gives the average distance between a typical observation and the mean of the dataset

empirical rule

Chebyshev's rule

for any number k > 1, at least (1-1/k^2) fraction of the data will like within k standard deviations of the mean

z-score

measures the relative position of an observation in comparison to the mean

outliers using z-score

z-score bigger than 3 or less than -3

Lower Quartile (Q1, QL)

25% of the observation are below this

Median (M, Q2)

same as median

Upper quartile (QU, Q3)

75% of the observations lie below this

5 number summary

minimum, lower quartiles, median, upper quartile, maximum

probability

study of randomness and uncertainty, numerical measure of change

law of large numbers

when an experiment is repeated a large number of times, under identical conditions, then the relative frequency of a particular "outcome" approached the actual probability of that "outcome"

Subjective Probability

probabilities are assigned on the basis of subjective judgment/belief of an individual

theoretical probability

basic outcomes of the process are defined

probabilities are assigned to the basic outcomes

using these, probabilities of compound events are computed

experiment

a process that yields a single outcome that cannot be predicted with certainty

sample point

basic outcome of an experiment

sample space

set up all possible outcomes of an experiment, denoted by S

event

any subset of the sample space

compound event

a composition of 2 or more events

venn diagrams

pictorial diagrams where the sample space is represented by a rectangle with sample points represented by solid dots inside the rectangle

events are drawn as circles within the rectangle

Mutually exclusive events

events that share no sample points

multiplicative rule

used to find probability of two events happening at the same time

independence

if probability of event A does not depend on whether event B has occurred or not

random variable

a variable that assigns a unique value to each outcome of the Sample space

discrete random variable

variable that takes either finitely many values or a countably infinite set of values

countable set

a set in one to one correspondence with integers

continuous random variable

set of possible values consist of one or more intervals on the number line

Probability Distribution

specification of the possible values and probability associated with each possible value of the discrete random variable

bernoulli

random variables can assume only two possible values 1 (success) and 0 (failure)

binomial experiment

identical trials are repeated and we are interested in number of certain outcomes