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Section 5: Measurements and Basic Statistics
Lean Six Sigma Black Belt
46
Business
Professional
03/06/2017

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Term
What are the 4 steps for data-driven problem solving?
Definition
1. Practical problem
2. Statistical problem
3. Statistical solution
4. Practical solution
Term
What is the practical problem?
Definition
Problem is stated in practical terms-billing errors cost us millions
Term
What is the statistical problem?
Definition
Express the practical problem as a statistical one.

What factors are significant predictors of billing errors?
Term
What is a statistical solution?
Definition
Obtain statistical solution using data analysis tools.

Inconsistency in the order filling process causes billing errors
Term
What is a practical solution?
Definition
Convert statistical solution to practical terms.

Simplify the billing process and train
Term
Statistics def.
Definition
The science (and art) of data-based decision-making
Term
Population def
Definition
The entire process output which we wish to draw a conclusion
Term
Sample def
Definition
The subset used to represent the population
Term
Random sample def
Definition
A sample drawn such that every member of the population has an equal chance of being selected
Term
Parameter
Definition
A quantity associated with the population
Term
Statistic
Definition
A quantity calculated from the sample
Term
What are the 2 types of statistical tools?
Definition
Descriptive
Inferential
Term
Descriptive statistics
Definition
aim to describe and summarize the important features of a population or process

graphical-charts, graphs etc
numerical-mean, median, mode
Term
Inferential statistics
Definition
Use sample data to help make comparisons or draw inferences on the overall population

Analysis tools
hypothesis testing
data modeling
Term
What is a enumerative study?
Definition
study aimed to answer questions about the current population like how many or in what proportion

focuses on historical rather than predictive
Term
Which type of statistic is used in enumerative studies?
Definition
Descriptive
Term
Analytical study
Definition
Answers questions like why or what are the causes of

Generalizes results to future states of the population
Term
Which statistical tool does analytical studies use?
Definition
both descriptive and inferential
Term
What are the 2 types of measurement?
Definition
Discrete
continuous
Term
Discrete measurement
Definition
representations of categories or attributes

people, cars, animals

good/bad
boy/girl
Term
Continuous measurement
Definition
derived from a scale or continuum that is infinitely divisible.

seconds, minutes, inches

measurement of time, temp, weight
Term
Attribute data
Definition
Data that is counted

discrete measurement term because they sort or count items based on attributes

-defects
Term
Variable data
Definition
Data that is measured

term for continuous measurement since they can take on infinite values within any 2 points
Term
Nominal
Definition
Groups are labels, no order
-profession
-color of car
Term
Ordinal
Definition
groups are a logical order

-small
-medium
-large
Term
Counts
Definition
Number of items or events
-# of new car sales in a week
-# of accidents in a year
Term
Continuous
Definition
Measurements made along a continuum
-gas mileage
-speed of pitched ball
Term
Pareto chart
Definition
Shows the relative frequency of defects in rank-order

Used to pick the low hanging fruits
Term
Weighted-pareto chart
Definition
Takes into account severity ratings in addition to frequency
Term
Histogram
Definition
Simple visual that conveys a lot of information
Term
Stratify
Definition
Divide data into groups to reveal sub-patterns to help pinpoint cause of variation.
Term
Specification limits
Definition
targets
there is both upper and lower limits
Term
Accuracy
Definition
Average that is close to the target
Term
Precise
Definition
A narrow spread
Term
Mean
Definition
Average of a distribution
Term
Sample mean
Definition
Sum of all observations
----------------------------
Total number of observations
Term
Median
Definition
Divides data to 2 halves-it's the value in the middle
Term
Mode
Definition
Most frequently occurring value in the set
Term
Common measurements of dispersion
Definition
Range
variance
standard deviation
Term
range
Definition
difference between the largest and smallest data in the set
Term
variance
Definition
average squared distance between mean and individual observations
Term
standard deviation
Definition
positive square-root of the variance
Term
Empirical Rule
Definition
68-95-99.7% rule

68% of values in the normal curve fall within one SD of the mean, 95% fall within 2 SD of the mean, and 99.7% fall within 3 SD
Term
Normal distribution
Definition
The x is the mean, median and mode
Term
Central limit theorem
Definition
As sample size increases, distribution of the mean tends to take the normal shape of the actual population
Term
What is z score
Definition
how many standard deviations the observed value is from the mean
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