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  • Data, Graphs, and MeasurementSome of Chapter 3

  • ObjectivesData CollectionData DescriptionGraphs and Displays

  • Data Collection PlanningBegin 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:Seek usefulness, not perfection!Data recording must be easy. Try to build it in to the process under study.Use sampling as part of the plan to collect the data.Design the form with the COLLECTORS needs in mind.Minimize possibility of errors.Provide clear, unambiguous directions.Use existing data whenever possible.Teach all the data collectors how to collect the data correctly.

  • Types of DataProportionsCountsAttributesContinuous DataDiscrete DataMeasurement instrument

  • Nominal categorical data counts of items that are grouped into qualitative categories (examples gender, race, color)3 quantitative measures:Ordinal categories arranged from smallest to largest, no set distance between categories; (example income number of employees)Interval measures on a numerical scale with equi-distant units, but no true zero point; averages are OK (temperature is best example)Ratio similar to interval variable but includes zero pt.Data Measurement Levels

  • Data Description - other wayQualitativeOpen ended questionsFocus groupsQuantitativeMeasurements (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*

  • Population MeanFor ungrouped data, the population mean is the sum of all the population values divided by the total number of population values:*

  • EXAMPLE Population Mean*

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

  • EXAMPLE Sample Mean*

  • The MedianThe 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.


  • Properties of the MedianThere 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. *

  • EXAMPLES - MedianThe 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.

    *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 ModeThe mode is the value of the observation that appears most frequently.


  • Example - Mode*

  • The Relative Positions of the Mean, Median and the Mode*

  • Frequency DistributionFirst look at dataDetermine frequency and relative frequencyExample

    CategoryCountRelative freqCum. Rel FreqAlways39.39.39Usually16.16.55Sometimes26.26.81Never19.191.0Missing0.001.0Total100

  • Grouped Data FrequenciesStep 1 : create Data arrayStep 2: Calculate number of classes using Sturges ruleStep 3: Calculate WidthStep 4: Determine BoundariesStep 5: Count FrequencyStep 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 diagramsFlowchartsPareto chartsRun chartsHistogramsControl chartsScatter diagrams

  • Cause-and-Effect Diagram (Fishbone) A Tool that helps identify, sort and display possible causes for a specific problemIt 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 conditionTo analyze existing problems so corrective action can be takenSort out and relate some of the interactions among the factors affecting a particular process

  • Fishbone DiagramWhy should we use a Fishbone Diagram?Helps determine the root causes of a particular problemEncourages group participationIdentifies problem areas efficientlyIndicates possible causes of variation in a processIncreases process knowledge

  • *Cause & Effect Diagram LLC

  • 2007Itasca Community College*Flowchart DiagramHigh level view of process flow6-12 steps usuallyShows major system components Useful starting point in complex projects

    Itasca Community College

  • *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

  • 2007Itasca Community College*From the organizations eyesCustomerorderMakeAssemblePackagePurchasematerialShipR & D designProductionengineeringQualityCostaccountingInformationsystemsMISDistributionStores &finishedgoodsPurchasing/receivingMasterproductionschedulingProductionplanningSales orderprocessingOutsideprocesses

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

    Study current conditions problem identification

  • Histogram ExampleA 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


  • Other Graphs and ChartsBar chartsGraphical representation of categorical data Length of bar represents frequency of observationsPie Charts A graph in shape of a circleSlices corresponds to classes or categoriesSize of slice is proportional to magnitudeStem and Leaf

  • Stem-and-Leaf

    One 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.


  • 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:


  • Stem-and-leaf: Another Example*

  • Dot PlotsA 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.


  • Constructing Line ChartsDraw 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.) 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.) 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 ExampleSuppose 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#31013141013151114161419211115171013141217191318201215171420231115171216181013141013141521241418217191419229121391213121517244

  • Line Chart