Statistics for BSN 3 something that can guide them in their analysis.pptx

The Continuous Improvement
Map
Control Charts
Mistake Proofing
Design of Experiment
Implementing
Solutions***
Group Creativity
Brainstorming
Cost Benefit Analysis
Planning & Project Management*
Managing Selecting & Decision Making
Risk
FMEA
PDPC
RAID Log*
Focus Groups
Observations
Understanding
Cause &
Effect
Pareto Analysis
Flowcharting IDEF0 Process Mapping
KPIs
Lean Measures
Fault Tree Analysis
Morphological Analysis
SCAMPER***
Matrix Diagram
Confidence Intervals
Pugh Matrix
Fishbone Diagram Relations Mapping SIPOC*
Paired Comparison
Prioritization Matrix
Interviews
Lateral Thinking
Hypothesis Testing
Reliability Analysis
Understanding
Performance**
Benchmarking***
Tree Diagram*
Attribute Analysis
Traffic Light Assessment Critical-to Tree
Kano Decision Balance Sheet
Risk Analysis*
Flow Process Charts** Service Blueprints
DMAIC
Run Charts 5 Whys
Cross Training
TPM
Automation
Kaizen Events Control Planning
ANOVA Chi-Square
Data collection planner*
Check Sheets
Questionnaires
Data
Collection
Probability Distributions
Capability Indices
Gap Analysis*
Bottleneck
Analysis
MSA
Descriptive Statistics
Cost of Quality*
Process Yield
Histograms
Graphical Analysis
Simulation Just in Time
5S Quick Changeover Visual
Management
Portfolio Matrix
TPN Analysis
Four Field Matrix
Root Cause Analysis Data Mining
How-How Diagram***
Sampling
Spaghetti **
Affinity Diagram
Mind Mapping*
PDCA
Designing & Analyzing Processes
Correlation
Scatter Plots Regression
Policy Deployment Gantt Charts
Daily Planning
PERT/CPM
MOST RACI Matrix Activity
Networks
SWOT Analysis
Stakeholder Analysis Project Charter
Improvement Roadmaps
Standard work Document control
A3 Thinking
Multi vari Studies
OEE
Earned Value
Value Stream Mapping**
Time Value Map**
Force Field Analysis
Payoff Matrix Delphi
Method
Decision Tree Pick Chart Voting
Suggestion systems Five Ws
Process Redesign
Break-even Analysis Importance-Urgency
Mapping
Quality Function Deployment
Waste Analysis**
Value Analysis**
Product Family Matrix Pull Flow
Ergonomics

 Statistics is concerned with the describing, interpretation and
analyzing of data.
 It is, therefore, an essential element in any improvement
process.
 Statistics is often categorized into descriptive and inferential
statistics.
 It uses analytical methods which provide
the math to model and predict variation.
 It uses graphical methods to help making
numbers visible for communication
purposes.
- Descriptive Statistics

Why do we Need Statistics?
 To find why a process behaves the way it does.
 To find why it produces defective goods or services.
 To center our processes on ‘Target’ or ‘Nominal’.
 To check the accuracy and precision of the process.
 To prevent problems caused by assignable causes
of variation.
 To reduce variability and improve process
capability.
 To know the truth about the real world.

Descriptive Statistics:
 Methods of describing the characteristics of a data set.
 Useful because they allow you to make sense of the data.
 Helps exploring and making conclusions about the data in order
to make rational decisions.
 Includes calculating things such as the average of the data, its
spread and the shape it produces.

 For example, we may be concerned about describing:
• The weight of a product in a production line.
• The time taken to process an application.

 Descriptive statistics involves describing, summarizing and
organizing the data so it can be easily understood.
 Graphical displays are often used along with the
quantitative
measures to enable clarity of communication.

 When analyzing a graphical display, you can draw conclusions
based on several characteristics of the graph.
 You may ask questions such ask:
• Where is the approximate middle, or center, of the graph?
• How spread out are the data values on the graph?
• What is the overall shape of the graph?
• Does it have any interesting patterns?

Outlier:
 A data point that is significantly greater or smaller than other
data points in a data set.
 It is useful when analyzing data to identify outliers

They may affect the calculation of
descriptive statistics.
 Outliers can occur in any given data set and in
any distribution.

Outlier:
 The easiest way to detect them is by graphing the data or using
graphical methods such as:
• Histograms.
• Boxplots.
• Normal probability plots.
*
●

Outlier:
 Outliers may indicate an experimental error or incorrect
recording of data.
 They may also occur by chance.
• It may be normal to have high or low data points.
 You need to decide whether to exclude them
before carrying out your analysis.
• An outlier should be excluded if it is due to
measurement or human error.

Outlier:
 This example is about the time taken to process a sample of
applications.
2.8 8.7 0.7 4.9 3.4 2.1 4.0
Outlier
0 1 2 3 4 5 6 7
8 9
It is clear that one data point is far distant from the rest of the values.
This point is an ‘outlier’

The following measures are used to describe a data set:
 Measures of position (also referred to as central tendency or
location measures).
 Measures of spread (also referred to as variability or
dispersion
measures).
 Measures of shape.

 If assignable causes of variation are affecting the process, we
will see changes in:
• Position.
• Spread.
• Shape.
• Any combination of the three.

Measures of Position:
 Position Statistics measure the data central tendency.
 Central tendency refers to where the data is centered.
 You may have calculated an average of some kind.
 Despite the common use of average, there are different
statistics by which we can describe the average of a data set:
• Mean.
• Median.
• Mode.

Mean:
 The total of all the values divided by the size of the data set.
 It is the most commonly used statistic of position.
 It is easy to understand and calculate.
 It works well when the distribution is symmetric and there are
no outliers.
 The mean of a sample is denoted by ‘x-bar’.
 The mean of a population is denoted by ‘μ’.
Mean
0 1 2 3 4 5 6 7 8 9

Median:
 The middle value where exactly half of the data values are
above it and half are below it.
 Less widely used.
 A useful statistic due to its robustness.
 It can reduce the effect of outliers.
 Often used when the data is nonsymmetrical.
 Ensure that the values are ordered before calculation.
 With an even number of values, the median is the mean of the
two middle values.
0 1 2 3 4 5 6 7 8 9
Median Mean

Median Calculation:
12
30
31
37
38
40
41
41
44
45
23
33
34
36
38
40
41
41
44
Median = 38 + 40 / 2 = 39

 Why can the mean and median be different?
0 1 2 3 4 5 6 7 8 9
Mean
Median

Mode:
 The value that occurs the most often in a data set.
 It is rarely used as a central tendency measure
 It is more useful to distinguish between unimodal and
multimodal distributions
• When data has more than one peak.

Measures of Spread:
 The Spread refers to how the data deviates from the position
measure.
 It gives an indication of the amount of variation in the
process.
• An important indicator of quality.
• Used to control process variability and improve quality.
 All manufacturing and transactional
processes are variable to some degree.
 There are different statistics by which
we can describe the spread of a data set:
• Range.
• Standard deviation.
Spread

Range:
 The difference between the highest and the lowest values.
 The simplest measure of variability.
 Often denoted by ‘R’.
 It is good enough in many practical cases.
 It does not make full use of the available data.
 It can be misleading when the data is skewed or in the presence
of outliers.
• Just one outlier will increase
the range dramatically.
0 1 2 3 4 5 6 7 8 9
Range

Standard Deviation:
 The average distance of the data points from their own mean.
 A low standard deviation indicates that the data points are
clustered around the mean.
 A large standard deviation indicates that they are widely
scattered around the mean.
 The standard deviation of a sample is
denoted by ‘s’.
 The standard deviation of a population
is denoted by “μ”.

Standard Deviation:
 Perceived as difficult to understand because it is not easy to
picture what it is.
 It is however a more robust measure of variability.
 Standard deviation is computed as follows:
Mean (x-bar)
s = standard deviation
x = mean
x = values of the data set
n = size of the data set
∑ ( x – x )2
s =
n - 1

Exercise:
 This example is about the time taken to process a sample of
applications.
 Find the mean, median, range and standard deviation for
the
following set of data: 2.8, 8.7, 0.7, 4.9, 3.4, 2.1 & 4.0.
Time allowed: 10 minutes

 If someone hands you a sheet of data and asks you to find the
mean, median, range and standard deviation, what do you do?
21 19 20 24 23 21 26 23
25 24 19 19 21 19 25 19
23 23 15 22 23 20 14 20
15 19 20 21 17 15 16 19
13 17 19 17 22 20 18 16
17 18 21 21 17 20 21 21
21 17 17 19 21 22 25 20
19 20 24 28 26 26 25 24

Measures of Shape:
 Data can be plotted into a histogram to have a general idea of
its shape, or distribution.
 The shape can reveal a lot of information about the data.
 Data will always follow some know distribution.

Measures of Shape:
 It may be symmetrical or nonsymmetrical.
 In a symmetrical distribution, the two sides of the distribution
are a mirror image of each other.
 Examples of symmetrical distributions include:
• Uniform.
• Normal.
• Camel-back.
• Bow-tie shaped.

Measures of Shape:
 The shape helps identifying which descriptive statistic is more
appropriate to use in a given situation.
 If the data is symmetrical, then we may use the mean or
median
to measure the central tendency as they are almost equal.
 If the data is skewed, then the median will be a more
appropriate to measure the central tendency.
 Two common statistics that measure the shape of
the data:
• Skewness.
• Kurtosis.

Skewness:
 Describes whether the data is distributed symmetrically around
the mean.
 A skewness value of zero indicates perfect symmetry.
 A negative value implies left-skewed data.
 A positive value implies right-skewed data.
X
X
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(+) – SK > 0 (-) – SK < 0

Kurtosis:
 Measures the degree of flatness (or peakness) of the shape.
 When the data values are clustered around the middle, then the
distribution is more peaked.
• A greater kurtosis value.
 When the data values are spread around more evenly, then the
distribution is more flatted.
• A smaller kurtosis values.
X
X
X
X
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X
(-) Platykurtic (0) Mesokurtic (+) Leptokurtic

 Skewness and kurtosis statistics can be evaluated visually via a
histogram.
 They can also be calculated by hand.
 This is generally unnecessary with modern statistical software
(such as Minitab).

Further Information:
 Variance is a measure of the variation around the mean.
 It measures how far a set of data points are spread out from
their mean.
 The units are the square of the units used for the original
data.
• For example, a variable measured in meters will have a variance
measured in meters squared.
 It is the square of the standard deviation.
Variance = s2

Further Information:
 The Inter Quartile Range is also used to measure
variability.
 Quartiles divide an ordered data set into 4 parts.
 Each contains 25% of the data.
 The inter quartile range contains the middle
50% of the data (i.e. Q3-Q1).
 It is often used when the data is not normally
distributed.
25%
Interquartile Range
25%
25%
25%
50%

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