QM 6640 MIDTERM
Calculate the odds against an event.
(1-P(A)) / P(A)
Define and calculate permutations.
An arrangement in a particular order of r randomly samples items from a group of n items. n!/(n-r)!
Define and calculate combinations.
An arrangement of r items chosen at random from n items where order is not important. n!/(r!(n-r)!)
Define the Empirical Rule.
68.26% lie within 1 standard deviation of the mean. 95.44% lie within 2 standard deviations. 99.73% lie within 3 standard deviations.
What is a Pareto chart?
A bar chart in which categories are displayed in descending order of frequency.
Define data set.
All the values of all the variables from all the observations chosen.
In a left skewed distribution, what is the relationship between median and mean?
Mean < Median
Define covariance.
The degree to which two variable change together.
List and explain common statistical pitfalls.
1. Conclusions from small samples. 2. Conclusions from nonrandom samples. 3. Conclusions from rare events. 4. Poor survey methods. 5. Assuming a causal link. 6. Generalization to individuals 7. Unconscious bias 8. Significance versus importance
List non-random sampling methods.
1. Judgement sample 2. Convenience sample 3. Focus groups
What are some common sources of error?
1. Nonresponse bias 2. Selection bias 3. Response error 4. Coverage error 5. Measurement error 6. Interviewer error 7. Sampling error (unavoidable)
List common graphing errors.
1. Nonzero origin 2. Elastic graph proportions 3. Dramatic titles or distracting pictures 4. 3-D and Novelty graphs 5. Rotated graphs 6. Complex graphs 7. Area trick
Define variable.
A characteristic of the subject or individual (ie employee's income)
Define ogive.
A line graph of cumulative frequencies.
Define frequency polygon.
A line graph that connects the midpoints of histogram intervals.
What is meant by left-skewed (negatively skewed)?
A longer left tail.
What is meant by right-skewed (positively skewed)
A longer right tail.
Define parameter.
A measurement or characteristic of a population.
Define statistic.
A numerical value computed from a sample.
Define observation.
A single member of a collection of items.
What is the Law of Large numbers?
AS the number of trials increases, any empirical probability approaches its theoretical limit.
Explain the uses of statistics in business.
Auditing Marketing Health Care Quality Improvement Purchasing Medicine Operations Management Product Warranty
What is the subjective approach to probability?
Based on informed opinion or judgement.
Define nominal data.
Categorical data where order does not matter (ie eye color)
Define descriptive statistics.
Collection, presentation, and summary of data.
List the reasons to study statistics.
Communication Computer Skills Information Management Technical Literacy Process Improvement
Define ratio data.
Continues data where 0 means none (ie accounts payable).
Define interval data.
Continuous data where zero does not mean none (ie temperature)
Define time series data set.
Each observation in the sample represents a different equally spaced point in time.
Define cross-sectional data.
Each observation represents a different individual unit at the same point in time.
What is the empirical approach to probability?
Estimated from observed outcome frequency.
When should you use a log scale?
For time series data that might be expected to grow at a compound annual percentage rate.
Define inferential statistics.
Generalizing from a sample to a population, estimating unknown parameters, drawing conclusions, and making decisions.
What is the special law of addition?
In the case of mutually exclusive events, the addition law reduces to P(A or B) = P(A) + P(B)
What is the classical approach to probability?
Known a priori by nature of the experiment.
Explain Kurtosis.
Kurtosis refers to the relative length of the tails and the degree of concentration of the center. Kurtosis < 0 = longer tails (Platykurtic) Kurtosis = 0 = Normal peak (Mesokurtic) Kurtosis > 0 = Sharper Peak (Leptokurtic)
What is the General Law of Multiplication?
P(A and B) = P(A given B) * P(B)
Calculate conditional probability.
P(A given B) = P(A and B)/P(B)
What is the General Law of Addition?
P(A or B) = P(A) + P(B) - P(A and B)
Calculate the odds in favor of an event.
P(A) / (1-P(A))
Estimate standard deviation from range.
R/6 For normal distribution, that range is roughly 6 std devs
Define ordinal data.
Rank has meaning, but there is no clear meaning to difference between ranks. (ie Likert Scale)
Explain systemic sampling.
Select every kth item from a list or sequence.
Explain cluster sampling.
Select random geographical regions (ie zip codes) that represent the population.
Explain stratified sampling.
Select randomly from within a defined strata (ie by age, occupation, gender).
Define standard deviation.
Square root of the variance.
Calculate coefficient of variation.
Standard deviation expressed as a percentage of the mean. (s/x_bar)*100% Useful for comparing variables measured in difference units.
Define variance.
Sum of squared deviations from the mean divided by population/sample size.
What are mutually exclusive events?
The intersection contains no elements. P(A and B) = 0
Define Chebyshev's Theorem.
The percentage of observations that lie within k standard deviations of the mean must be at least 100(1-1/k^2). (ie k = 2 standard deviations, 75% of population lies within mean +/- 2(sigma))
Define statistics.
The science of collecting, organizing, analyzing, interpreting, and presenting data.
Explain collectively exhaustive events.
The union of events is the entire sample space.
Explain random sampling.
Use random numbers to select items from a list.
When are two events independent?
When the occurrence or non-occurrence of one does not affect the chances of the other occurring. P(A given B) = P(A)
What is a standardized variable?
Z, redefines each observation in terms of the number of standard deviations from the mean. Positive Z = observation to right of mean Negative Z = observation to left of mean Unusual if Z > 2 Outlier if Z > 3
