E370 Exam 1 (Chapters 1-5)at Indiana University

A frequency distribution shows

the number of data observations that fall into specific intervals (classes)

Relative frequency distributions display

the proportion of observations in each class relative to the total number of observations

A cumulative relative frequency distribution

totals the proportion of observations that are less than or equal to the class at which you are looking

Discrete Data

can be counted/ whole numbers

Continuous data

can be measured/ can be any value

Ideally, the number of classes in a frequency distribution should be between

4 and 20

k is the

number of classes in a frequency distribution

Estimated class width formula

(max value-min value)/k

Class boundaries

Maximum and minimum values in each class

Coningency tables allow you to compare

the effects of multiple variables

Scatterplots show

the relationship between 2 variables

Elements

the entities on which data are collected

Variable

characteristic of interest for the elements

Observation

Set of measurements obtained for a particular element

Nominal

No ranking, Eye color, zip codes

Ordinal

Ranking, Education level

Interval

No true zero, Calendar year

Ratio

True zero, Income

Time Series

Data values that correspond to specific measurements taken over a range of time periods

Cross Section

Data values collected from a number of subjects during a single time period

Descriptive statistics

Collecting, summarizing, and displaying data

Inferential statistics

making claims or conclusions about the data based on a sample (makes statement about population)

Parameter

a described characteristic about a population

Statistic

a described characteristic about a sample

A sample statistic is referred to as the ________ of the corresponding population parameter.

point estimator

The median is ________________ to outliers

not sensitive

If the data have exactly two modes, the data are ___________•If the data have more than two modes, the data are ____________

bimodal, multimodal

Left skewed

mean

Right-skewed

mean > median

variance

squared standard deviation

standard deviation

square root of variance

Coefficient of variation

(Sample SD/sample mean)X100

A high CV indicates _______________ relative to the mean

high variability

z-score

Identifies the number of standard deviations a particular value is from the mean of its distribution

Positive z-score

above the mean

Negative z-score

below the mean

z-score of outliers

+3 or -3

Percentiles

measure the approximate percentage of values in the data set that are belowthe value of interest

60th percentile = 31.1 MPG

60% of cars in the sample have MPG < 31.1

Sample covariance, sxy

measures the direction of the linear relationship between two variables

A positive sample covariance value implies a

positive linear relationship

Sample correlation coefficient, rxy

measures both the strengthand directionof the linear relationship between two variables

The values of sample correlation coefficient r range from -1.0, ____ , to +1.0, ___________

a strong negative relationship, a strongpositive relationship

Probability

a numerical measure of the likelihood that an event will occur

Experiment

any process that generates well-defined outcomes

sample space for an experiment

set of all experimental outcomes

event

a collection of outcomes

Classical Method

Assigning probabilities based on the assumption of equally likely outcomes

Empirical Method

Assigning probabilities based on experimentation or historical data

Subjective Method

Assigning probabilities based on judgment or experience

Law of Large Numbers (LLN)

As the number of trails or observations increases, the observed probability of an event (empirical probability) approaches theoretical (classical) probability

complement of event A

the event consisting of all outcomes that are NOT in A; area out of circle

union of events Aand B

the event containing all outcomes that are in A or B or both: whole venn diagram

union of events Aand B is denoted by

A(smile)B

complement of A is denoted by

A'

intersection of events A and B

the set of all outcomes that are in both A and B; middle of venn diagram

The intersection of events Aand B is denoted by

A(frown)B

mutually exclusive

the events have no outcomes in common

Conditional Probability

The probability of an event given or knowing that another event has occurred

The conditional probability of A given B is denoted by

P(A|B)

P(A|B) is calculated by

P(A and B)/P(B)

Two events are considered independent if

the occurrence of one event has no impact on the occurrence of the other event

random variable

a numerical description of the outcome of an experiment

expected value

multiply valueXprobability then add all of them together and average it

variance calculation

- figure out how much each score differs (deviates) from the mean by subtracting the mean from each score

- square each of these deviation values (to get rid of negative value)

- multiply by their own probabilities

- add together

The characteristics of a Binomial Experiment

fixed number of trials, Each trial has only two possible outcomes, Each trial is independent of the other trials in the experiment

Meanof a Binomial Distribution

μ= np

Standard Deviation of a Binomial Distribution

σ=SQROOT(npq)