Business Statistics

the methodology of extracting useful information from a data set.

Statistics

To do good statistical analysis, you must

1. Find the right data.

2. Use the appropriate statistical tools.

3. Clearly communicate the numerical

information into written language.

Consists of all items of interest.

Population

A subset of the population

Sample

The more dispersion of data across a graph

Standard deviation

What are the two types of Quantitative data?

Discrete: Countable
Continuous: measurable

What are the two branches of statistics?

Descriptive & Inferential Statistics

This branch of statistics deals with collecting, organizing, and presenting the data.

Descriptive statistics

This branch of statistics deals with drawing conclusions about a population based on sample data from that population.

Inferential statistics

A _____ statistic is calculated from the _____ data and is used to make ______ about the unknown population

parameter.

Sample, sample, inferences

What are the five types of data?

1. Cross-sectional

2. Time series

3. Structured

4. Unstructured

5. Big

This type of data is collected by recording a characteristic of many subjects at the same point in time, or without regard to differences in time.

Cross sectional

In cross sectional data subjects may include what?

Individuals , Households, firms, industries, regions, and countries.

This type of data is collected by recording a characteristic of a subject over several time periods.

Time series

Time series data subjects may include what?

hourly, daily, weekly, monthly, quarterly, or annual observations.

This type of data has a well-defined length and format.

Structured data

Subjects for structured data includes

Numbers, dates, strings of words, etc.

This type of data does not conform to a predefined row -column format.

Unstructured data

Subjects for unstructured data include.

Reports, emails, multimedia, etc.

This type of data has a massive volume of data that is difficult to manage, process, and analyze using traditional tools.

Big data

A _____ is the general characteristic

being observed on objects of interest.

variable

What are the two types of variables?

Qualitative - Non numerical

Quantitative - Numerical

What are the two types of quantitative variables?

Discrete and Continuous

A ______ variable assumes a

countable number of distinct values.

discrete

A ______ variable can assume an uncountable number of values within an interval.

continuous

What are the two scales of measure for qualitative variables?

Nominal & ordinal

What are the two scales of measure for quantitative variables?

Interval & Ratio

What scale of measure is categorized for grouping the data?

nominal scale

What scale of measure may be categorized and ranked

with respect to some characteristic or trait.

Ordinal scale

What scale of measure has NO starting point.

Interval scale

What scale of measure has a starting point

Ratio Scale

A _________ for qualitative data groups data into categories and records how many observations fall into each category.

frequency distribution

For relative frequency you divide the number of objects observed by the ______

Sample size

Objects that don’t share anything any common are ______

Mutually exclusive

If objects take up the whole space then they are ______

exhaustive

For each category’s ______ count the number of them that fall in that category.

Frequency

To calculate relative frequency, you divide each category’s frequency by the _______.

sample size

To express relative frequencies in terms of percentages, multiply each proportion by ___.

100

All proportions in relative frequency must sum to___ , and total of percentages must sum to ___

1.0, 100%

a ______ is a segmented circle whose segments portray the relative frequencies of the categories of a qualitative variable.

Pie chart

A ______ depicts the frequency or the relative frequency for each category of the qualitative data as a series of horizontal or vertical bars which are proportional to the values that are to be depicted.

Bar chart

A _________ for quantitative data groups data into intervals called classes, and records the number of observations that fall into each class.

frequency distribution

When constructing frequency distribution the two guidelines are classes are ______ ______ & ________

mutually exclusive, exhaustive

The formula for approximating the class width is what?

Largest value - Smallest Value/ Number of classes

This image of data converted is known as what?

Frequency distribution

A _______ _______ ______ specifies how many observations fall below the upper limit of a particular class.

Cumulative Frequency Distribution

The third column represents the what?

Cumulative frequency

A _____ _____ _____ identifies the proportion or fraction of values that fall into each class.

relative frequency distribution

A ______ ______ _____ distribution gives the proportion or fraction of values that fall below the upper limit of each class.

Cumulative relative frequency

A ______ is a visual representation of a

frequency or a relative frequency distribution.

Histogram

In a histogram the bar height represents the respective class

frequency or ______ ______

relative frequency

This image refers to

Symmetric Distribution

If the data is displayed as a long, narrow tail to

the right it is what?

Positively skewed

If the data is displayed as a long, narrow tail to the left it is what?

Negatively skewed

A ________ is used to determine if two

variables are related.

scatter plot

What is the term for upward or downward-sloping

trend of the data?

Linear relationship (positive or Negative)

Data that has _______ is randomly scattered with

no discernible pattern.

no relationship

The______ ____is a primary measure of central

location.

arithmetic mean

what is the formula for the median?

n+1/2

If median is not listed and falls between two observations, ____ then divide by 2

add

____ is the term for the most frequently appeared data.

Mode

When using any type of rate or rate of return, use _______ ____

geometric mean

Another term for arithmetic mean is simply ____ or _______

mean, average

What are the four measures of central location?

mean, median, mode, weighted average

This picture represents the _____.

median

Sometimes, a data set can have either one mode, __ _____ or ____ _____

no mode, many modes

The weighted mean is used when some observations have ______.

worth

What are the four measures of dispersion?

Range
Mean Absolute Deviation
Variance and standard deviation
Coefficient of Variant

What is the formula for the range?

Max value - min value

The ____ _______ _______ represents the average of the absolute differences

between the observations and the mean.

Mean Absolute deviation

a ______ is a numerical value that measures the likelihood that an uncertain event occurs

probability

All possible outcomes is known as what?

Sample space

“A or B” in problem, then use _____ sign

union

“A and B” in problem, then use _____ sign

intersection

An _______ is process that leads to one of

several possible outcomes.

experiment

Something is an experiment because the outcome is _______.

unknown

S is denoted as _____ _____

sample space

An _____ is a subset

of the sample space.

event

The green represents a _____ of S, therefore it is an _____

subset, event

The _____ of two events (A∪B) is the event

consisting of all simple events in A or B.

Union

The ____________ of two events (A ∩ B) consists of all outcomes in A and B.

intersection

The ______ of event A (i.e., Ac) is the event consisting of all outcomes in the sample space S that are not in A.

complement

When listing Unions and intersections don’t list the data _____

twice

What are the two general types of probabilities?

Subjective and objective

This type of probability is assigned on personal and subjective judgment.
Or as Professor Park said, your own belief.

subjective probability

What are the two types of objective probabilities?

Empirical and classical

This type of objective probability has a relative frequency of

occurrence.

empirical probability

This picture represents what probability?

empirical probability

deduced by reasoning about the problems. It is based on the assumption that all outcomes of an experiment are equally likely.

Classical probability

When converting an odds ratio to a probability, if odds FOR event A are “a to b” then use the formula….

a/a+b

When converting an odds ratio to a probability, if odds AGAINST event A are “a to b” then use the formula …

b/ a+b

These formulas represent converting an ____ ratio to a _______

odds, probability

When converting a probability to an odds ratio, the odds for event A occurring equal what formula?

P(A) / 1- P(A)

When converting a probability to an odds ratio, the odds against event A occurring equal what formula?

1-P(A) / P(A)

This rule is when the probability of the complement of an event, P

(A^c), is equal to one minus the probability of the

event.

The Complement rule

What is the formula for the complement rule?

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

This rule is when the probability that event A or B occurs, or that

at least one of these events occurs

Addition rule

what is the formula of the addition rule?

P(A ∪ B) = P( A) + P(B) - P(A ∩B)

The probability of an event GIVEN that another

event has already occurred.

Conditional probability

This image is the addition rule for ___ ______ _____ events

two mutually exclusive