# Business Statistics [Maymester – Midterm]

**Flashcard maker :**Lily Taylor

Statistics (Definition)

…the science of collecting, organizing, analyzing, interpreting, and presenting data. Some experts prefer to call statistics data science, a trilogy of tasks involving data modeling, analysis, and decision making.

Statistic (Definition)

…a single measure, reported as a number, used to summarize a sample data set.

Descriptive Statistics (Definition)

…a single measure, reported as a number, used to summarize a sample data set.

Inferential Statistics (Definition)

…generalizing from a sample to a population, estimating unknown population parameters, drawing conclusions, and making decisions

Pitfalls of Statistics (List)

Pitfall 1: Conclusions from Small Samples

Pitfall 2: Conclusions from Nonrandom Samples

Pitfall 3: Conclusions from Rare Events

Pitfall 4: Poor Survey Methods

Pitfall 5: Assuming a Causal Link

Pitfall 6: Generalization to Individuals

Pitfall 7: Unconscious Bias

Pitfall 8: Significance versus Importance

Pitfall 2: Conclusions from Nonrandom Samples

Pitfall 3: Conclusions from Rare Events

Pitfall 4: Poor Survey Methods

Pitfall 5: Assuming a Causal Link

Pitfall 6: Generalization to Individuals

Pitfall 7: Unconscious Bias

Pitfall 8: Significance versus Importance

Statistics vs. Probability

Statistics summarizes history, while probability quantifies future uncertainty.

Observation (Definition)

…a single member of a collection of items that we want to study, such as a person, firm, or region.

Variable (Definition)

…a characteristic of the subject or individual, such as an employee’s income or an invoice amount

Data Set (Definition)

…consists of all the values of all of the variables for all of the observations we have chosen to observe.

Univariate Data Set (Definition, Example and Typical Tasks)

One variable; Ex: Income; Typical Tasks: Histogram, descriptive statistics, frequency tallies.

Bivariate Data Set (Definition, Example, and Typical Tasks)

Two variables; Ex: Income and age; Typical Tasks: Scatter plots, correlations, regression modeling…

Multivariate Data Set (Definition, Example, and Typical Tasks)

More than two variables; Ex: Income, age and gender; Typical Tasks: multiple regression, data mining, econometric modeling…

Categorical Data (Verbal Label, Coding and Binary Values)

(also called qualitative data); have values that are described by words rather than numbers.

Verbal Labeling: cars are called small, mid-sized, sudan, etc…

Coding: numbers can represent words; i.e. 1=cash, 2=check, 3=credit card.

Binary Values: variables only have two values (i.e. employed and unemployed).

Verbal Labeling: cars are called small, mid-sized, sudan, etc…

Coding: numbers can represent words; i.e. 1=cash, 2=check, 3=credit card.

Binary Values: variables only have two values (i.e. employed and unemployed).

Numerical Data (Discreet and Continuous Data)

(also called quantitative data – statistics or tables) counting, measuring something, or some kind of mathematical operation – provides insight into characteristics of a data set using mathematics.

Discreet Data: takes on a numerical value – you can count it on your fingers (no negatives – only integers).

Continuous Data: number might represent a percentage of customers out of an entire group surveyed – can take on fractional values.

Discreet Data: takes on a numerical value – you can count it on your fingers (no negatives – only integers).

Continuous Data: number might represent a percentage of customers out of an entire group surveyed – can take on fractional values.

Times Series Data vs. Cross Sectional Data

Time Series Data: each observation in the sample represents a different equally spaced point in time (i.e. years, months, days…) – we are interested in trends and patterns over time.

Cross Sectional Data: each observation represents a different individual unity at the same point in time – we are interested in variation among observations.

We can combine the two data types to get pooled cross sectional and time series data.

Cross Sectional Data: each observation represents a different individual unity at the same point in time – we are interested in variation among observations.

We can combine the two data types to get pooled cross sectional and time series data.

Levels of Measurement (List)

Nominal

Ordinal

Interval

Ratio

Ordinal

Interval

Ratio

Nominal Data (Definition)

(Latin from “name”) identifying categories only; i.e. eye color (blue, brown, green, etc…)

Ordinal Data (Definition)

Rank has meaning; no clear meaning to distance; i.e. full sized, compact, subcompact.

Interval Data (Definition)

Distance has meaning; i.e. temperature.

Ratio Data (Definition)

Meaningful zero exists; i.e. accounts payable – 20$ is twice as much as 10$ (ratio of 2:1) – 0 point means the absence of something.

Likert Scales (Describe)

Example: “College-bound high school students should be required to study a foreign language – Check one box.”

Box Options: “Strongly Agree,” “Somewhat Agree,” “Neither Agree Nor Disagree,” “Somewhat Disagree,” “Strongly Disagree”…

Box Options: “Strongly Agree,” “Somewhat Agree,” “Neither Agree Nor Disagree,” “Somewhat Disagree,” “Strongly Disagree”…

Parameter (Definition)

a measurement or characteristic of the population (i.e. a mean or proportion). Usually unknown since we can rarely observe the entire population; i.e. a census of a certain target population is impossible – so these parameters would be estimated using a sample.

Target Population (Definition)

…the population that we’re interested in.

Sampling Frame (Definition)

… the group from which we take the sample; i.e. phone books, directories, email addresses from a certain online newsletter, etc…

Sampling Methods (List)

1. Simple Random Sample

2. Systematic Sample

3. Stratified Sampling

4. Cluster Sampling

5. Judgement Sample

6. Convenience Sample

7 Focus Groups

2. Systematic Sample

3. Stratified Sampling

4. Cluster Sampling

5. Judgement Sample

6. Convenience Sample

7 Focus Groups

Simple Random Sample (Describe)

… use random numbers to select items from a list.

Systematic Sample (Describe)

… select every n-th item from a list or sequence (e.g., restaurant customers); every fifth car gets randomly pulled over.

Stratified Sampling (Describe)

… select randomly within defined strata (e.g. by age, occupation, gender)…

Cluster Sampling (Describe)

… like stratified sampling except strata are geographical areas (e.g. zip codes)… trying to find locations in their particular market.

Judgement Sample (Describe)

… use expert knowledge to choose “typical” items (e.g. which employees to interview for yearly reviews).

Convenience Sample (Describe)

… use a sample that happens to be given (e.g. a coworker that just happens to be at lunch with you).

Focus Groups (Describe)

… in-depth dialogue with a panel of representative or specific individuals (i.e. iPod users).

Basic Steps to Survey Research (List)

Step 1: State the goals of the research.

Step 2: Develop the budget (time, money, staff).

Step 3: Create a research design (target population, frame, sample size).

Step 4: Choose a survey type and method of administration.

Step 5: Design a data collection instrument (questionnaire).

Step 6: Pretest the survey instrument and revise as needed.

Step 7: Administer the survey (follow up if needed).

Step 8: Code the data and analyze it.

Step 2: Develop the budget (time, money, staff).

Step 3: Create a research design (target population, frame, sample size).

Step 4: Choose a survey type and method of administration.

Step 5: Design a data collection instrument (questionnaire).

Step 6: Pretest the survey instrument and revise as needed.

Step 7: Administer the survey (follow up if needed).

Step 8: Code the data and analyze it.

Visual Data Representation

(charts and graphs) provides insight into characteristics of a data set without using mathematics.

Stem and Leaf Plot

…a tool of exploratory data analysis (EDA) that seeks to reveal essential data features in an intuitive way. A stem-and-leaf plot is basically a frequency tally, except that we use digits instead of tally marks. For two-digit or three-digit integer data, the stem is the tens digit of the data, and the leaf is the ones digit.

Dot Plots

A dot plot is the simplest graphical display of n individual values of numerical data – pretty much like a stem-and-leaf plot, but instead of digits, it uses dots.

A stacked dot plot compares two dot plots (stacked on top of one another).

A stacked dot plot compares two dot plots (stacked on top of one another).

Left Skewed Histogram

… negatively skewed, with a long left “tail.”

Right Skewed Histogram

… positively skewed, with long right “tail.”

Symmetric Histogram

… both “tails” are the same length.

Pareto Charts

… special type of bar chart used in quality management to display the frequency of defects or errors of different types; categories are displaced in descending order of frequency.

Calculate the Mean

… add up all of the numbers, and then divide by how many numbers there were.

=AVERAGE(Data)

=AVERAGE(Data)

Calculate the Median

… the 50th percentile, or midpoint, of the sorted sample data.

=MEDIAN(Data)

=MEDIAN(Data)

Calculate the Mode

… the most frequently occurring data value; i.e. 2 2 5 5 5 6 7 8 8… 5 is the mode.

=MODE.SNGL(Data)

=MODE.SNGL(Data)

Calculate the Midrange

the point halfway between the lowest and highest values of x.

[x(1) + x(2)] / 2

= (MIN(Data)+MAX(Data))/2

[x(1) + x(2)] / 2

= (MIN(Data)+MAX(Data))/2

Trimmed Mean

… gets rid of outliers, used for economic data. Remove the highest and lowest k percent of the observation.

=TRIMMEAN(Data, 0.1)

=TRIMMEAN(Data, 0.1)

Sample Standard Deviation (S)

=STDEV.S(Data); A low standard deviation indicates that the data points tend to be very close to the mean; high standard deviation indicates that the data points are spread out over a large range of values.

Mean Absolute Deviation (MAD)

… reveals the average distance from the center. Appealing because of its simple interpretation.

=AVEDEV(Data)

=AVEDEV(Data)

Range

Max(Data) – Min(Data).

Empirical Rule

The Empirical Rule states that for data from a normal distribution, we expect the interval ? Â± k? to contain a known percentage of data.

Method of Medians

… find the median of all of the data – then, find the two medians of the upper and lower sections of the original median.

Level of Confidence (Definition)

… a measure of how confident we are in a given marin of error; i.e. 90% level of confidence that an estimate based on a sample will differ by no more than 1.6 standard errors from the “true” population value because of sampling error.

Random Experiment (Definition)

… an observational process whose results cannot be known in advance.

Sample Space (Definition)

… the set of all outcomes (S) of a random experiment.

Discrete Sample Space (Definition)

… a sample space with a countable number of outcomes; i.e. grades; A to F; the probabilities of all simple events must sum to 1.

Continuous Sample Space (Definition)

… the sample space cannot be listed but can be described by a rule; i.e. the sample space for the length of a randomly chosen cell phone call would be S={all X such that X>0}, because you don’t know how long cell phone calls can be.

Event (Definition)

… any subset of outcomes in the sample space.

Simple Event / Elementary Event (Definition)

(“Elementary, my dear Watson!” – which Sherlock Holmes never ACTUALLY said, by the way); a single outcome.

Probability (Definition)

… the probability of an event is a number that measures the likelihood that the event will occur; the probability of event A must lie within the interval from 0-1.

Empirical Approach (Definition)

…use the empirical or relative frequency approach to assign probabilities by counting the frequency of observed outcomes defined on the experimental sample space – based on HISTORICAL DATA; i.e. default rates on student loans:

P(a student defaults)= f/n = (number of defaults / number of loans)

P(a student defaults)= f/n = (number of defaults / number of loans)

The Law of Large Numbers (Definition)

… says that as the number of trials increases, any empirical probability approaches its theoretical limit; i.e. flip a coin 50 times; we would theoretically expect the proportion of heads to be near .50.

Classical Approach [A priori] (Definition)

A priori: the process of assigning probabilities before the event is observed or the experiment is conducted; based on logic not experience; Think “priori = PRIOR.”

Instead of performing the experiment, we can use deduction to determine the probability of an event.

Instead of performing the experiment, we can use deduction to determine the probability of an event.

Subjective Approach (Definition)

… reflects someone’s informed judgement about the likelihood of an event; used when there is no repeatable random experiment; i.e. What is the probability that the price of Ford’s stock will rise within the next 30 days?

Complement of an Event (Definition)

… of an event A is denoted by A’ and consists of everything in the sample space S except event A.

Union of Two Events (Definition)

… consists of all outcomes in the sample space S that are contained either in event A or in event B, or in both.

Intersection of Two Events (Definition)

… the event consisting of all outcomes in the sample space S that are contained in both events A and B.

Mutually Exclusive Events (Definition)

… two events are mutually exclusive if their intersection is the null set which contains no elements.

Special Law of Addition (Definition)

… in the case of mutually exclusive events, the addition law reduces to: P(A) + P(B).

Collectively Exhaustive Events (Definition)

… if their union is the entire sample space S; there can be more than two collectively exhaustive events, as long as they take up the entirety of sample space S.

Conditional Probability (Definition)

… the probability of an event A given that event B has occurred; i.e.:

P(A in Physics) = 0.2

P(A in Calculus) = 0.2, so…

P(A in Physics | A in Calculus) = 0.8

P(A in Physics | C in Calculus) = 0.15

P(A in Physics) = 0.2

P(A in Calculus) = 0.2, so…

P(A in Physics | A in Calculus) = 0.8

P(A in Physics | C in Calculus) = 0.15

Independent Events (Definition)

Event A is independent of event B if the conditional probability P(A | B) is the same as the marginal probability P(A).

Contingency Table (Definition)

… also called a cross-tabulation table; used often when gathering empirical data.

NOTE: Learn how to create / read / analyze contingency tables – MUY IMPORTANTE.

NOTE: Learn how to create / read / analyze contingency tables – MUY IMPORTANTE.

Random Variable (Definition)

… a function or rule that assigns a numerical value to each outcome in the sample space of a random experiment.

Uppercase letters (X, Y, etc…) represent random variables.

Lowercase letters (x, y, etc…) represent values of random variables.

Uppercase letters (X, Y, etc…) represent random variables.

Lowercase letters (x, y, etc…) represent values of random variables.

Discrete Random Variable (Definition)

… a variable that has a countable number of distinct values.

Discrete Probability Distribution

… assigns a probability to each value of a discrete random variable X.

Calculating the Variance

… (x-mu)^2

So, X minus the average of the xP(x) value.

So, X minus the average of the xP(x) value.

Probability Distribution Function (PDF)

… a mathematical function that shows the probability of each X-value.

Cumulative Distribution Function (CDF)

… a mathematical function that shows the cumulative sum of probabilities, adding from the smallest to the largest X-value, gradually approaching unity; i.e…

x | CDF

1 | .2

2 | .2 + .3

3 | .2 + .3 + .4

x | CDF

1 | .2

2 | .2 + .3

3 | .2 + .3 + .4

Bernoulli Experiments

… a random experiment with only 2 outcomes; one outcome is labeled “success” (x=1) and the other a “failure” (x=0).

Success is defined as the less likely outcome.

Success is defined as the less likely outcome.

Binomial Distribution (Definition)

… arises when a Bernoulli experiment is repeated “n” times; each trial is independent.

Binomial Distribution

=BINOM.DIST(x, n, ?, 0 or 1).