【正文】 mperature ? Calendar years ? Program task calendar ? Length in inches ? Minutes for time duration ? Frequency count like defects per unit ? Percentage number as in market share Quantitative data is monly referred to as continuous data. 79 Data Summary Data Qualitative (attribute) Quantitative (continuous) ? Minimum of 2 variable values ? Finite number of variable values ? No information between variable values ? Potentially any value ? Values have equal units ? Information exists between variables Quantitative (continuous) data yield the most information. Project Information Continuum Low High 80 Data Impact on Project The lack of data is a failure mode in project pletion success. ?Without data, decision for actions to implement are at risk: F Makes situation worse F Incurs unnecessary cost F Decreases customer satisfaction ?If you cannot collect data, and money cannot be spent to collect data, the value of the project is in question. 81 Data Set Evaluation Begin by asking three simple questions: ? What variable value occurs most? ? What variable is the midpoint? ? What is the spread of the variable values? How do you extract knowledge from a data set ? To answer the questions, look at the frequency distribution, which is a count of how frequently a variable value occurs within a data set. 82 Frequency Table A frequency table is used to condense and summarize a set of data. The table contains the elements of class interval, midpoint, frequency, and relative frequency. Class Interval is range of variable values used to tally the count or frequency of occurrence. The number and size of the class intervals are dependent on: Number of Classes Generally between 5 and 20 classes are used Note: Rules to create interval classes include : 1) Easy for reader to interpret 2) Narrow enough to reveal interesting detail 3) Wide enough to show data “pile up” 4) Coincide data with interval midpoint Boundary Values where “nooverlapping occurs” of variable values Width of Each Class choose the same width for each class. The choice of number of classes and the width are dependant. Approx. Class Width =Max. Data Min Data Number of classes Brigade Field Exercise Data of 50 Shots (Inches) EXAMPLE ? 12 classes chosen ? Decimal values from to to prevent overlap ? Width of class set at 1 inch 102 108 107 108 107107 111 102 105 102107 105 109 107 103108 107 107 105 106105 111 108 103 106109 104 109 108 111103 104 112 105 103110 113 110 107 105106 113 106 106 108109 111 108 107 108C la s s I n t e r v a l1 0 1 .6 – 1 0 2 .51 0 2 .6 – 1 0 3 .51 0 3 .6 – 1 0 4 .51 0 4 .6 – 1 0 5 .51 0 5 .6 – 1 0 6 .51 0 6 .6 – 1 0 7 .51 0 7 .6 – 1 0 8 .51 0 8 .6 – 1 0 9 .51 0 9 .6 – 1 1 0 .51 1 0 .6 – 1 1 1 .51 1 1 .6 – 1 1 2 .51 1 2 .6 – 1 1 3 .583 Frequency Table (cont.) ? Midpoint is the middle of the class interval. ? Frequency is the count of occurrences within the class interval. (Note: frequency should sum to total data set) Brigade Field Exercise Data of 50 Shots (Inches) EXAMPLE ? Midpoints are 102,103, etc… ? The number of times values fall within interval are counted and listed. ? The Rf is calculated based on a total quantity of 50. 102 108 107 108 107107 111 102 105 102107 105 109 107 103108 107 107 105 106105 111 108 103 106109 104 109 108 111103 104 112 105 103110 113 110 107 105106 113 106 106 108109 111 108 107 108Mi d p o int Fr e q u e n c yR e lati v eFr e q u e n c y102 3 0 . 0 6103 4 0 . 0 8104 2 0 . 0 4105 6 0 . 1 2106 5 0 . 1 0107 9 0 . 1 8108 8 0 . 1 6109 4 0 . 0 8110 2 0 . 0 4111 4 0 . 0 8112 1 0 . 0 2113 2 0 . 0 4To t a l 50 1 . 0 0Relative frequency (Rf) is the occurrence as pared to the entire set of class intervals. R f = Frequency Qty in Data set (Note: Rf always sums to ) 84 Frequency Table (cont.) Brigade Field Exercise Data of 50 Shots General Rules to Form Table 1) Determine the largest and smallest numbers and find the difference between the two numbers. 2) Divide the difference found in step 1 into a convenient number of class intervals. (Note: Usually between 5 20, try to coincide midpoint values to reduce assignment errors.) 3) Check to make sure boundary values do not coincide (overlap) with data set values. 4) Assign frequency of occurrences to the intervals using a tally or score sheet. Compare totals as a check. 5) Calculate Relative frequency. Method C las s I n t e r v a l Mi d p o int Fr e q u e n c yR e lati v eFr e q u e n c y1 0 1 .6 – 1 0 2 .5 102 3 0 . 0 61 0 2 .6 – 1 0 3 .5 103 4 0 . 0 81 0 3 .6 – 1 0 4 .5 104 0 01 0 4 .6 – 1 0 5 .5 105 8 0 . 1 61 0 5 .6 – 1 0 6 .5 106 6 0 . 1 21 0 6 .6 – 1 0 7 .5 107 8 0 . 1 61 0 7 .6 – 1 0 8 .5 108 8 0 . 1 61 0 8 .6 – 1 0 9 .5 109 4 0 . 0 81 0 9 .6 – 1 1 0 .5 110 2 0 . 0 41 1 0 .6 – 1 1 1 .5 111 4 0 . 0 81 1 1 .6 – 1 1 2 .5 112 1 0 . 0 21 1 2 .6 – 1 1 3 .5 113 2 0 . 0 4To t a l 50 1 . 0 085 The Histogram 0123456789Frequency101 102 103 104 105 106 107 108 109 110 111 112 113IntervalsA histogram is the graphical representation of a Frequency Distribution. Brigade Field Exercise Data of 50 Shots ? Histograms show general shapes: Symmetry Clusters Spreads Gaps Outliers ? Are used to graph counts, frequency, and/or relative frequency data (Usually on the vertical (y) axis) ? Show possible data values as class intervals. (Usually on the horizontal (x) axis) ? Help facilitate class interval sizing appropriateness. ? Shows fo