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```Six Sigma
Green Belt
Core Data Displays

-6
-4
-2
0
2
4
6
Sigma Quality Management
1
Six Sigma
Green Belt
Variation in Product or Service
 Leaving the World of Averages and Entering the World of Dispersion
 Coin Toss Exercise:
Flip
1
2
3
4
5
6
7
8
9
10
Result
(H or
T)
2
Data and Statistics Concepts
Six Sigma
Green Belt
 Nature of Data – Measurement vs. Count Data
 Single Point Measures of Performance
•Central Tendency
•Variability
3
Central Tendency
Measure
Mean
Description & Use
The Average of a set of numbers. The most commonly used measure of
the data’s center.
Remember, when you calculate an average, about half of the raw data
will be above and half will be below the average - this does not translate
into one half good and one half bad!!
Median
The midpoint of a set of numbers placed in rank order.
The median is a preferred measure of the data's center when there are
very large or small values, i.e. when the data is skewed.
Mode
The most frequently appearing number(s) in a set of data. Useful when
data displays wide variation, perhaps due to mixed processes.
Six Sigma
Green Belt
How to Calculate
n
x
x
i
i 1
n
where:
 is the symbol for "sum of"
n is the number of data, and
xi are the data values
for an odd number of data:
x( n1)/ 2
for an even number of data:
x n 2 1  x n 2
2
For the data set:
1,2,2,3,3,3,3,4,4,5,5,6,7
three is the mode
4
Variability
Measure
Range
Description & Use
The difference between the largest and smallest values in a data set.
Variance
The sum of the squared differences of the data from the mean, divided
by the number of data less one. Forms the basis for the standard
deviation.
Standard
Deviation
The square root of the variance. This is the “best” measure of variability,
since it considers all the data from the sample. The Standard Deviation
can be thought of as a “distance” measure - showing how far the data are
away from the mean value.
Six Sigma
Green Belt
How to Calculate
R  xmax  xmin
n
s2 
(x  x )
2
i
i 1
n 1
s  s2
5
Line Graphs
Six Sigma
Green Belt
1. Draw a vertical and a horizontal axis on a piece of graph paper.
2. Label the vertical axis with the variable being plotted.
3. Label the horizontal axis with the unit of time or order in which the
numbers were collected (i.e. Day 1, 2, 3, . . ., Customer 1, 2, 3, . . .
etc.).
4. Determine the scale of the vertical axis. The top of this axis should be
about 20 percent larger than the largest data value. The bottom of this
axis should be about 20 percent lower than the smallest data value.
This let’s you see the best picture of the process’ variability. Label the
axis in convenient intervals between these numbers.
5. Plot the data values on the graph number by number, preserving the
order in which they occurred.
6. Connect the points on the graph.
7. (Optional) Calculate the mean of the data and draw this as a solid line
through the data. This turns the line graph into a run chart - trends
and patterns are often easier to see with a run chart.
6
Six Sigma
Green Belt
Line Graph
Errors per 1000 Orders
10
8
Errors
6
4
2
0
1
3
5
7
9
11
13
15
17
19
Orders (1000)
7
Six Sigma
Green Belt
Run Chart
Defects/Unit
Good
Defects
18
16
14
12
10
8
6
4
2
0
1
3
5
7
9
11
13 15 17 19 21 23 25
Data Collected:
7/29-8/3
A. J. Carr
Unit Number
8
Six Sigma
Green Belt
Interpretation
Mean
(Center Line)
1
3
5
7
9
11
13
15
17
19
Mean
1
3
5
7
9
11
13
15
17
19
Mean
Also: Extreme Values
1
3
5
7
9
11
13
15
17
19
9
Decisions in the Face of Variation
Six Sigma
Green Belt
Correct Decisions:
1. Only Common Cause Variation Present
2. Common and Assignable Cause Variation
Present
Errors:
1. Just Common Cause Variation Present – NOT!
2. Assignable Cause Variation Present – NOT!
10
Six Sigma
Green Belt
Variation Decision - Summary
“Our” Interpretation
“True” Situation
Only Common Causes
Only Common
Causes
Common Plus
Assignable
Causes
Correct Decision – If Process is
Not Capable, Act to Understand
Process Variables and Improve
Process
Wrong Decision – You Are
Ignoring Possible Opportunities
to Eliminate Assignable Causes
from the Process
Common Plus
Assignable Causes
Wrong Decision – You are
Overreacting to Point -to-Point
Variation!
Correct Decision – Understand
and Eliminate Assignable
Causes from Process
11
Six Sigma
Green Belt
Bar Chart Examples
100
90
80
Sales Volum es by Region by Qtr
70
60
50
40
30
Missing Patient Documentation by Nursing Unit
Percentage
Missing 30
(%)
Date: Nov, Dec
By: F.N. Gale, RN
East
West
North
20
10
0
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
20
10
3West
3 North
2 North
2 West
Unit
Megawat t
Hours
Elect ricit y Product ion Growt h
by Year and Fuel
Gas
Coal
Oil
Nuclear
Year
12
Six Sigma
Green Belt
Percent
98
Survival Rate - Open Heart Surgery by Hospital
Three “Worst”
97
D
H
I
Hospital
13
Six Sigma
Green Belt
Pie Chart
Pie Chart of PC Printer Errors - Model PH-6
Garbled
Font
6
Other
12
Low Memory
Wrong
12
Font
48
Extra
Sheet
Fed 18
Paper Jam
32
14
Six Sigma
Green Belt
Power
1
0.9
0.8
Handling
0.7
0.6
Comfort
0.5
0.4
0.3
0.2
0.1
0
Style
Safety
Price
Economy
15
Chart Comparison
Six Sigma
Green Belt
Chart
Line Graph
Makes trends and data variation over time easy to
track. Good for highlighting changes in some
variable. Can be used to track more than one
variable at a time.
Can lead to “overreaction” to changes that aren’t
really there. Control charts are the best tools for
studying variation.
Bar Chart
Good for comparing one category to another. Many
different styles can be constructed (stacked bar, “3dimensional” bar chart, etc.) Easy to construct.
Sometimes inappropriately used for tracking data
over time. Similar danger to overreaction as line
graph.
Pie Chart
Useful for showing relative proportion of each
Should not be used for tracking data over time.
category to the whole. Several layers of stratification
can be shown on one graph.