Statistics

5!=

120

Marginal Probability

NA

Operations management

Distribution of inventory items in a big box store

Finance

Risk assessment of an investment

Probability distribution function

(PDF) mathematical function that shows the probability of each X-value. P(X=x)

The probability of any x value of a discrete distribution is:

0<=x<=1

The sum of the probabilities of all the outcomes in the sample space is

1

True or false: managers want to see detailed numerical explanations in technical reports

False, managers are busy and want numbers summarized in context

True or False: Distributions of business data are typically (but not always) left skewed

False. Most business data is bounded on the left by zero so the data tends to be right skewed.

Marketing

Identifying repeat customers

Where should a graph or table be placed in a report

In the narrative, near the paragraph in which they are cited

Uniform

N/A

Statistics

The science of collecting, organizing, analyzing, interpreting, and presenting data.

The rectangles of a histogram:

are drawn with no space/gaps between them, represent grouped data, represent the class width and frequency or relative frequency of the respective class

Discrete random variable:

arises from counting something such as the number of customer arrivals in the next minute

Sum of repeated bernoulli trials

binomial random variable

A log scale is useful for:

financial data that is expected to grow rapidly

Characteristics of a bar chart include:

length or height of bar reflects frequency of a category, display horizontal bars when axis labels are long or there are many categories

Histograms can be used to:

observe group data, determine the shape of data, observe the spread of the variability of data

How many outcomes of an experiment constitute a simple event?

one

Expected value of discrete random variable

sum of all X values weighted by their respective probabilities

The mean of the Bernoulli distribution (pi symbol) is called

the probability of success

A pie chart is a segmented circle whose segments must sum to a _____________.

total

A stacked column chart requires that the column height be a _____________ of at least two subtotals

total

Cumulative distribution function

(CDF) shows the cumulative sum of probabilities, adding from the smallest to largest X value. P(X<=x)

Binomial distribution symmetric

(Pi symbol)=0.5

Binomial distribution skewed right

(pi symbol)<0.5

Binomial distribution skewed left

(pi symbol)>0.5

In the binomial distribution which expression represents the probability of failure?

1-(pi symbol)

Generally, a negative covariance between market demands indicates:

A centralized distribution center will decrease the aggregate demand variance, a centralized distribution center can reduce the need for safety stock

Which of the following should one look for when identifying a hypergeometric application?

A finite population (n), and a known number of success (s)

Symmetrical

A histogram with evenly distributed tails

Probability

A numerical value that measure the likelihood of an uncertain event occurring

A priori or classical probability

A probability that can be deduced through logical reasoning before an experiment is performed

Bernoulli experiment

A random experiment with only two outcomes

Auditing

A sample of errors from invoice statements

An outlier is defined as:

An extreme value that is located in the tail of the histogram, an extreme value that might have arisen from a different cause, an extreme value that might have arisen from measurement error

The empirical rule

Approximately 95% of values fall within 2 standard deviations of the mean for data with bell shaped histogram

Ways statistics is used

Auditing, Marketing, Health Care, Quality Improvement, Purchasing, Medicine, Operations Management, Product Warranty,

Order of constructing a polygon

Construct a Frequency Distribution, Find the midpoint for each interval of the frequency distribution, the midpoints are plotted based on the frequency or relative frequency for the respective class, neighboring midpoints are connected together by a straight line.

Rules for a data analyst

Follow accepted procedures, Maintain data integrity, protect confidential information

Characteristics of binomial distribution

For each trial the probability of success remains the same, each trial only has two possible outcomes, each trial is independent of the previous trial

Which variables can be displayed on a log scale?

GDP, Real estate values in a fast growing market

The normal distribution is also called the

Gaussian distribution

Exhaustive

In probability theory and logic, a set of events is jointly or collectively exhaustive if at least one of the events must occur. For example, when rolling a six-sided die, the outcomes 1, 2, 3, 4, 5, and 6 are collectively exhaustive, because they encompass the entire range of possible outcomes

The multiplication rule is used to calculate what type of probability

Joint Probability

Negatively Skewed

Left skewed, a histogram with a left tail that is longer than the right tail

Dependent event

NA

Empirical Probability

NA

Independent event

NA

Joint Probability

NA

Sample space

NA

Subjective Probability

NA

The excel normal CDF for area to the left of a given x value

NORM.DIST

Excel Normal Inverse function for X value of a given cumulative area:

NORM.INV

The excel normal CDF for area to the left of a z score is

NORM.S.DIST

Excel Normal Inverse function for Z score of a given cumulative area:

NORM.S.INV

There are several guidelines that one should follow when creating graphs, what describes these guidelines?

Novelty graphs such as pyramid charts increase ambiguity, axes should be clearly labeled, axes that are numerical should be to the appropriate scale

If the odds AGAINST event A are quoted as b to a, then the implied probability of event A is

P(A)= A/(A+B)

_____________ charts are used to sort out the vital few from the trivial many.

Pareto

Positively Skewed

Right skewed, a histogram with a right tail that is longer than the right tail

Headings in an effective table display:

Should be simple and descriptive, not detailed and complex

Standard Deviation formula for percent and number?

Square root of (n*%)*(1-%)

What characteristic is not a rule of thumb for displaying categorical data on a column chart?

The height of each column should be the same: in reality the height of each column should be proportional to the quality displayed

To calculate the variance of the sum of two independent random variables:

The individual variances are summed

When determining the approximate width of the bins for a frequency distribution of quantitative data, the difference of what two values is divided by the number of bins?

The maximum and the minimum value

The normal distribution is described by

The population mean and the population standard deviation

Conditional Probability

The probability of an event "A" given that event "B" has occurred: represents the chance of an event occurring when focusing on a subset of the total sample

General law of addition states that

The probability of the union of two events A and B is: P(A or B)= P(A) + P(B) - P(A and B) BECAUSE when you add the P(A) and P(B) together, you could the P(A and B) twice, So you have to subtract the P(A and B) to avoid overstating the probability.

A relative frequency distribution for quantitative data identifies:

The proportion of observations that occur in each bin

Variance of a continuous random variable

The variance is the weighted average of the squared deviations of the mean, the standard deviation is the square root of the variance, the variance cannot be negative

Data analysis can help identify the difference between real and perceived ethical problems (true or false)

True

Successful businesses expect their employees to have some knowledge of statistics (true or false)

True

Independence

Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. Ex) two tosses of a coin

What is NOT a common error one should beware

Unembellished charts that do not contain sound and animation, should not contain bc distracting

The letter used to denote the standard normal random variable

Z

Cumulative frequency distributions show the:

accumulated counts up to and including the current bin as the bin limits increase

Continuous random variable:

arises from measuring something such as the waiting time until the next customer arrives, a continuous random variable can have decimal values

Discrete Probability Distribution

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

Which statistical pitfall does the following statement match: People who belong to health clubs tend to have college degrees therefore exercise increases your IQ

assuming a casual link

To be regarded as a candidate for normality, a random variable should:

be measured on a continuous scale, possess a clear center, have only one peak, exhibit tapering tails, be symmetric about the mean

One of the primary goals of constructing a frequency distribution for quantitative data is to summarize the data:

by showing frequency of values that lie within a class or bin

The _______ formula is used to determine the number of different ways to arrange a group of X objects from a total of N objects and the order of objects is irrelevant

combination

An ogive is useful for:

comparing shapes of known distributions, finding percentiles

For any given event, the sum of the probability of that event and the probability of its __________ must equal 1

compliment

A random variable with an equally likely chance of assuming any value within a specified range is said to have which distribution?

continuous uniform distribution

Discrete Random Variable

countable number of distinct values

Discrete Uniform distribution

describes a random variable with a finite number of integer values from a to b. each value of the random variable is equally likely to occur.

Mutually exclusive event

ex.) flipping a coin and getting heads and tails in one toss

Criteria for hypergeometric applications

finite population (N), containing a number of successes (s) and sampling without replacement (n) where the probability of success is not constant

Corporate recruiters rank ethics and personal integrity _____________ on the list in hiring criteria

first

Binomial application factors

fixed number of trials (n), there are only two outcomes success or failure, the probability of success for each trial is constant, trials are independent, the random variable (X) is the number of successes

More precise interval

increase sample size, decrease confidence level

Conclusions from small samples

na

assuming a casual link

na

conclusions from rare events

na

unconscious bias

na

The _________ formula is used to determine the number of ways to arrange x objects from a group of n objects where the order of the objects matter

permutation

A trial or process that produces several possible outcomes that cannot be known in advance is called an

random experiment

Discrete Uniform Distribution

random variable with a finite number of consecutive integer values from a to b, the distribution is symmetric, the probability of each value of the random variable is the same

Inferential Statistics

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

Descriptive Statistics

refers to the collection, organization, presentation, and data (either using charts and graphs or using a numerical summary, tables of numerical data)

When a researcher wants to know the proportion of all observations that fall within a particular bin they would need the:

relative frequency distribution

A line chart can be used to

spot trends, display time series data

estimator

statistic used to infer value for parameter

Variance of discrete random variable

sum of the squared standard deviations about its expected value, weighted by the probability of each X-value

General Law of Addition

the probability of the union of two events A and B is the sum of their probabilities less the probability of their intersection: P(A or B)= P(A)+P(B)-P(A and B)

Contingency Tables are useful to analyze

the results of a survey, relative frequency

Random variables are represented by _________________ letters while particular values of random variables are represented by ___________________ letters

uppercase, lowercase

To approximate the binomial distribution with the normal distribution let

μ=n(π), σ=(square root of):nπ(1-π)