Data, Graphs, and MeasurementSome of Chapter 3

Objectives

•Data Collection•Data Description•Graphs and Displays

Data Collection Planning•Begin by answering these key questions:

▫ Why are you collecting the data?▫ What data analysis tool do we see using to display

data after we have it? Run chart is recommended for displaying data

showing performance of a process over time.▫ What type of data do we need?▫ Where and when will the data be collected?▫ Who will collect the data?▫ How can we collect the data with minimum effort

and chance of error? Put operational definitions of data to be collected

somewhere on the data collection form – for example noting that “Surgery Start time” is defined as when the first incision is made.

Keep the following in mind when planning for data collection:

1. Seek usefulness, not perfection!2. Data recording must be easy. Try to build

it in to the process under study.3. Use sampling as part of the plan to collect

the data.4. Design the form with the COLLECTOR’S

needs in mind.5. Minimize possibility of errors.6. Provide clear, unambiguous directions.7. Use existing data whenever possible.8. Teach all the data collectors how to

collect the data correctly.

Types of Data

• Proportions• Counts• Attributes

Continuous Data Discrete Data

Measurement instrument

Nominal –categorical data– counts of items that are grouped into qualitative categories (examples – gender, race, color)

3 quantitative measures:o Ordinal – categories arranged from smallest to

largest, no set distance between categories; (example – income number of employees)

o Interval – measures on a numerical scale with equi-distant units, but no true zero point; averages are OK (temperature is best example)

o Ratio – similar to interval variable but includes zero pt.

Data Measurement Levels

Data Description - other way

•Qualitative▫Open ended questions▫Focus groups

•Quantitative▫Measurements (times, counts)▫Likert scale surveys

•*Environmental

Characteristics of the MeanThe arithmetic mean is the most widely

used measure of location. It requires the interval scale. Its major characteristics are:▫All values are used.▫It is unique.▫It is calculated by summing the values

and dividing by the number of values.▫Can be affected by extreme values

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Population Mean

For ungrouped data, the population mean is the sum of all the population values divided by the total number of population values:

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EXAMPLE – Population Mean

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Sample Mean

• For ungrouped data, the sample mean is the sum of all the sample values divided by the number of sample values:

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EXAMPLE – Sample Mean

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The Median•The Median is the midpoint of the values after they have been ordered from the smallest to the largest.▫ For an odd set of values, there are as

many values above the median as below it in the data array.

▫ For an even set of values, the median will be the arithmetic average of the two middle numbers.

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Properties of the Median•There is a unique median for each

data set.• It is not affected by extremely large

or small values and is therefore a valuable measure of central tendency when such values occur.

• It can be computed for ratio-level, interval-level, and ordinal-level data.

• It can be computed for an open-ended frequency distribution if the median does not lie in an open-ended class.

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EXAMPLES - Median

The ages for a sample of five college students are:21, 25, 19, 20, 22

Arranging the data in ascending order gives:

19, 20, 21, 22, 25.

Thus the median is 21.

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The heights of four basketball players, in inches, are:

76, 73, 80, 75

Arranging the data in ascending order gives:

73, 75, 76, 80.

Thus the median is 75.5

The Mode

•The mode is the value of the observation that appears most frequently.

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Example - Mode

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The Relative Positions of the Mean, Median and the Mode

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Frequency Distribution

First “look” at dataDetermine frequency and relative frequency

Example

Category Count Relative freq

Cum. Rel Freq

Always 39 .39 .39

Usually 16 .16 .55

Sometimes 26 .26 .81

Never 19 .19 1.0

Missing 0 .00 1.0

Total 100

Grouped Data Frequencies

•Step 1 : create Data array•Step 2: Calculate number of classes using

Sturges’ rule•Step 3: Calculate Width•Step 4: Determine Boundaries•Step 5: Count Frequency•Step 6: Plot in a Histogram for continuous

data

W. Edward Deming recommends the use of the following tools:•Securing reliable information is an

important part of problem solving and decision making. Cause-and-effect diagrams Flowcharts Pareto charts Run charts Histograms Control charts Scatter diagrams

Cause-and-Effect Diagram (Fishbone)• A Tool that helps identify, sort and

display possible causes for a specific problem

•It graphically illustrates the relationship between a given outcome and all the factors that influence that outcome

Fishbone DiagramWhen should a team use a Fishbone

Diagram?•To identify root causes, the basic reasons

for a specific effect, problem or condition•To analyze existing problems so

corrective action can be taken•Sort out and relate some of the

interactions among the factors affecting a particular process

Fishbone Diagram

Why should we use a Fishbone Diagram?•Helps determine the root causes of a

particular problem•Encourages group participation• Identifies problem areas efficiently• Indicates possible causes of variation in a

process• Increases process knowledge

25Cause & Effect Diagram Example

MoreSteam.com LLC

2007Itasca Community College

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Flowchart Diagram

•High level view of process flow•6-12 steps usually•Shows major system components •Useful starting point in complex projects

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Flowchart Symbols= A Diamond indicates a Decision Point

= A rectangle indicates a Process

= An oval indicates the beginning or end of a process

= Arrows indicate the direction of flow

= A Parallelogram indicates input or output of information

= A modified rectangle indicates a document

2007 Itasca Community College

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From the organization’s eyes

Customerorder Make

AssemblePackage

Purchasematerial

Ship

R & D design

Productionengineering

Quality

Costaccounting

Informationsystems

MIS

DistributionStores &finishedgoods

Purchasing/receiving

Masterproductionscheduling

Productionplanning

Sales orderprocessing

Outsideprocesses

Histogram Chart

•Use if you want to determine which category of item, you focus your efforts on.

Study current conditions – problem identification

Histogram Example

A team decided to use Histogram method to display data the data collected on EKG turnaround times.

The team collected data for 32 days.

Sample Data Table: EKG Turnaround Time

9 16 1 4

15 8 13 1

13 16 14 17

7 2 20 2

2 2 18 3

17 2 14 20

1 1 2 7

1 2 15 2

Other Graphs and Charts

•Bar charts▫Graphical representation of categorical

data ▫Length of bar represents frequency of

observations•Pie Charts

▫A graph in shape of a circle▫Slices corresponds to classes or categories▫Size of slice is proportional to magnitude

•Stem and Leaf

Stem-and-LeafOne technique that is used to display

quantitative information in a condensed form is the stem-and-leaf display.

Stem-and-leaf display is a statistical technique to present a set of data. Each numerical value is divided into two parts. The leading digit(s) becomes the stem and the trailing digit the leaf. The stems are located along the vertical axis, and the leaf values are stacked against each other along the horizontal axis.

Advantage of the stem-and-leaf display over a frequency distribution - the identity of each observation is not lost.

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Stem-and-Leaf – ExampleSuppose the seven observations

in the 90 up to 100 class are: 96, 94, 93, 94, 95, 96, and 97.

The stem value is the leading digit or digits, in this case 9. The leaves are the trailing digits. The stem is placed to the left of a vertical line and the leaf values to the right. The values in the 90 up to 100 class would appear as

Then, we sort the values within each stem from smallest to largest. Thus, the second row of the stem-and-leaf display would appear as follows:

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Stem-and-leaf: Another Example

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Dot Plots• A dot plot groups the data as little as

possible and the identity of an individual observation is not lost.

• To develop a dot plot, each observation is simply displayed as a dot along a horizontal number line indicating the possible values of the data.

• If there are identical observations or the observations are too close to be shown individually, the dots are “piled” on top of each other.

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Constructing Line Charts

1.Draw and label the vertical (y) axis using the measurement units you are tracking (e.g., numbers of defectives, mean diameter, number of graduates, percent defective, etc.)

2.Draw and label the horizontal (x) axis to reflect the sequence in which the data points are collected (e.g., week 1, week 2, ... or 8AM, 9AM, 10AM, etc.)

3.Plot the data points on the chart in the order in which they became available and connect the points with lines between them.

Line Chart Example

•Suppose you identified that one waste in the process is long waiting times for patients. You decide to collect data to determine how much time should you allow for physician treatment. You feel this would help for better scheduling.

•A visit to a clinic reveals that there are 3 physicians treating patients.

Physician

#1 #2 #3

10 13 14

10 13 15

11 14 16

14 19 21

11 15 17

10 13 14

12 17 19

13 18 20

12 15 17

14 20 23

11 15 17

12 16 18

10 13 14

10 13 14

15 21 24

14 18 21

7 1 9

14 19 22

9 12 13

9 12 13

12 15 17

2 4 4

Line ChartTreatment Times

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Day

Min

ute

s Physician1

Physician2

Physician3

Line Chart – observe the trend for call times over time. Suppose call times were reduced by a process improvement.

Case B

Case C

Process improvement

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Diagnostic Charts

There are a variety of diagnostic techniques available to investigate quality problems. Two of the more prominent of these techniques are Pareto charts and fishbone diagrams.

Directions for Pareto

1. Collect Data2. Order Categories according to

magnitude of effect3. Write frequency of error next to

category and determine grand total.4. Calculate Cumulative % for each

category5. Draw and label Y axis with unit of

comparison6. Draw and label X axis with categories7. Draw on graph a line graph of

cumulative %8. Analyze the “vital few” in the 80% of

all errors

Pareto DiagramError Type Freq. % Cum.

%

Generic vs. Manuf. Label

44 41.9 41.9

Drug out of stock

20 19.05 60.95

Cannot Read Order

17 16.19 77.14

Physician Revised Medications

17 16.19 93.33

Complete Medication

7 6.67 100

Total 105 100

Using Pareto Chart to focus on cause

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Fishbone DiagramsAnother diagnostic chart is a cause-

and-effect diagram or a fishbone diagram. It is called a cause-and-effect diagram to emphasize the relationship between an effect and a set of possible causes that produce the particular effect.

This diagram is useful to help organize ideas and to identify relationships. It is a tool that encourages open brainstorming for ideas. By identifying these relationships we can determine factors that are the cause of variability in our process.

The name fishbone comes from the manner in which the various causes and effects are organized on the diagram. The effect is usually a particular problem, or perhaps a goal, and it is shown on the right-hand side of the diagram. The major causes are listed on the left-hand side of the diagram.

Using the 5 Whys tool:•Write down the specific problem.•Ask Why problem happens and write

down the answer•If the answer doesn’t identify root cause

then repeat.•Keep repeating until team is in agreement

that problem’s root cause is identified.

Root

Cause

.

Contrib. Cause

Direct Cause

Event

Contrib. Cause

Root Cause Chain (5 Why’s)

I was late to work today

WHY?

Because my car did not start.

WHY?

Because the car battery was dead.

Because the car door was open and dome light on.

WHY?

WHY?Because the door lock was not working correctly.

SOLUTION: Fix the door locking mechanism on the car.

Boxplot - Example49

Boxplot Example

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Describing Relationship between Two Variables

One graphical technique we use to show the relationship between variables is called a scatter diagram.

To draw a scatter diagram we need two variables. We scale one variable along the horizontal axis (X-axis) of a graph and the other variable along the vertical axis (Y-axis).

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Describing Relationship between Two Variables – Scatter Diagram Examples

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