# Part 2 Descriptive Statistics: Tabular and Graphical Methods

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Condensing Qualitative Data. Recurrence DistributionRelative Frequency Percent Frequency DistributionBar GraphPie Chart. Recurrence Distribution. A recurrence conveyance is a plain rundown of information demonstrating the recurrence (or number) of things in each of a few nonoverlapping classes.The target is to give bits of knowledge about the information that can't be immediately acquired by taking a gander at the first

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﻿Part 2 Descriptive Statistics: Tabular and Graphical Methods Summarizing Qualitative Data Summarizing Quantitative Data Exploratory Data Analysis Crosstabulations and Scatter Diagrams

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Summarizing Qualitative Data Frequency Distribution Relative Frequency Percent Frequency Distribution Bar Graph Pie Chart

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Frequency Distribution A recurrence dispersion is an unthinkable outline of information demonstrating the recurrence (or number) of things in each of a few nonoverlapping classes. The goal is to give bits of knowledge about the information that can't be immediately gotten by taking a gander at the first information.

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Example: Marada Inn Guests remaining at Marada Inn were solicited to rate the quality from their facilities as being incredible , better than expected , normal , underneath normal , or poor . The evaluations gave by a specimen of 20 missions are demonstrated as follows. Beneath Average Above Average Above Average Above Average Above Average Above Average Below Average Below Average Poor Poor Above Average Excellent Above Average Average Above Average Average Above Average

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Example: Marada Inn Frequency Distribution Rating Frequency Poor 2 Below Average 3 Average 5 Above Average 9 Excellent 1 Total 20

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Relative Frequency Distribution The relative recurrence of a class is the portion or extent of the aggregate number of information things having a place with the class. A relative recurrence appropriation is an unthinkable synopsis of an arrangement of information demonstrating the relative recurrence for each class.

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Percent Frequency Distribution The percent recurrence of a class is the relative recurrence duplicated by 100. A percent recurrence conveyance is an unthinkable synopsis of an arrangement of information demonstrating the percent recurrence for each class.

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Example: Marada Inn Relative Frequency and Percent Frequency Distributions Relative Percent Rating Frequency Poor .10 10 Below Average .15 15 Average .25 25 Above Average .45 45 Excellent .05 5 Total 1.00 100

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Bar Graph A reference diagram is a graphical gadget for delineating subjective information. On the even hub we determine the marks that are utilized for each of the classes. A recurrence , relative recurrence , or percent recurrence scale can be utilized for the vertical hub. Utilizing a bar of settled width drawn over each class name, we amplify the stature suitably. The bars are isolated to underline the way that each class is a different classification.

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9 8 7 6 Frequency 5 4 3 2 1 Rating Above Average Excellent Poor Below Average Example: Marada Inn Bar Graph

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Pie Chart The pie outline is an ordinarily utilized graphical gadget for exhibiting relative recurrence circulations for subjective information. To begin with draw a circle ; then utilize the relative frequencies to subdivide the hover into areas that compare to the relative recurrence for each class. Since there are 360 degrees around, a class with a relative recurrence of .25 would expend .25(360) = 90 degrees of the circle.

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Exc. 5% Poor 10% Below Average 15% Above Average 45% Average 25% Quality Ratings Example: Marada Inn Pie Chart

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Example: Marada Inn Insights Gained from the Preceding Pie Chart One-portion of the clients studied gave Marada a quality rating of "better than expected" or "superb" (taking a gander at the left half of the pie). This may satisfy the administrator. For every client who gave a "great" rating, there were two clients who gave a "poor" rating (taking a gander at the highest point of the pie). This ought to disappoint the director.

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Summarizing Quantitative Data Frequency Distribution Relative Frequency and Percent Frequency Distributions Dot Plot Histogram Cumulative Distributions Ogive

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Example: Hudson Auto Repair The supervisor of Hudson Auto might want to show signs of improvement photo of the circulation of expenses for motor tune-up parts. An example of 50 client solicitations has been taken and the expenses of parts, adjusted to the closest dollar, are recorded beneath.

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Frequency Distribution Guidelines for Selecting Number of Classes Use in the vicinity of 5 and 20 classes. Informational indexes with a bigger number of components more often than not require a bigger number of classes. Littler informational collections for the most part require less classes.

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Frequency Distribution Guidelines for Selecting Width of Classes Use classes of equivalent width. Inexact Class Width =

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Example: Hudson Auto Repair Frequency Distribution If we pick six classes: Approximate Class Width = (109 - 52)/6 = 9.5  10 Cost (\$) Frequency 50-59 2 60-69 13 70-79 16 80-89 7 90-99 7 100-109 5 Total 50

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Example: Hudson Auto Repair Relative Frequency and Percent Frequency Distributions Relative Percent Cost (\$) Frequency 50-59 .04 4 60-69 .26 26 70-79 .32 32 80-89 .14 14 90-99 .14 14 100-109 .10 Total 1.00 100

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Example: Hudson Auto Repair Insights Gained from the Percent Frequency Distribution Only 4% of the parts expenses are in the \$50-59 class. 30% of the parts expenses are under \$70. The best rate (32% or just about 33%) of the parts expenses are in the \$70-79 class. 10% of the parts expenses are \$100 or more.

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Dot Plot One of the least complex graphical outlines of information is a speck plot . A level pivot demonstrates the scope of information qualities. At that point every information esteem is spoken to by a speck set over the hub.

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. . .. . . . . .. .. .. .. . . . . . ..... .......... .. . .. . . ... . .. . 50 60 70 80 90 100 110 Cost (\$) Example: Hudson Auto Repair Dot Plot

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Histogram Another normal graphical introduction of quantitative information is a histogram . The variable of intrigue is put on the level pivot. A rectangle is drawn over each class interim with its stature comparing to the interim's recurrence , relative recurrence , or percent recurrence . Dissimilar to a reference diagram, a histogram has no common partition between rectangles of adjoining classes.

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Example: Hudson Auto Repair Histogram 18 16 14 12 Frequency 10 8 6 4 2 Parts Cost (\$) 50 60 70 80 90 100 110

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Cumulative Distributions Cumulative recurrence dissemination - demonstrates the quantity of things with qualities not exactly or equivalent to the furthest reaches of each class. Aggregate relative recurrence dispersion - demonstrates the extent of things with qualities not exactly or equivalent to the furthest reaches of each class. Aggregate percent recurrence dissemination - demonstrates the rate of things with qualities not exactly or equivalent to the furthest reaches of each class.

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Example: Hudson Auto Repair Cumulative Distributions Cumulative Cumulative Relative Percent Cost (\$) Frequency < 59 2 .04 4 < 69 15 .30 30 < 79 31 .62 62 < 89 38 .76 76 < 99 45 .90 90 < 109 50 1.00 100

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Ogive An ogive is a diagram of a combined dispersion. The information qualities are appeared on the level pivot. Appeared on the vertical pivot are the: aggregate frequencies, or combined relative frequencies, or total percent frequencies The recurrence (one of the above) of each class is plotted as a point. The plotted focuses are associated by straight lines.

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Example: Hudson Auto Repair Ogive Because as far as possible for the parts-cost information are 50-59, 60-69, et cetera, there have all the earmarks of being one-unit holes from 59 to 60, 69 to 70, et cetera. These crevices are disposed of by plotting focuses somewhere between as far as possible. Hence, 59.5 is utilized for the 50-59 class, 69.5 is utilized for the 60-69 class, et cetera.

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Example: Hudson Auto Repair Ogive with Cumulative Percent Frequencies 100 80 60 Cumulative Percent Frequency 40 20 Parts Cost (\$) 50 60 70 80 90 100 110

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Exploratory Data Analysis The systems of exploratory information investigation comprise of straightforward number juggling and simple to-draw pictures that can be utilized to abridge information rapidly. One such procedure is the stem-and-leaf show .

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Stem-and-Leaf Display A stem-and-leaf show indicates both the rank request and state of the conveyance of the information. It is like a histogram on its side, however it has the benefit of demonstrating the real information values. The primary digits of every information thing are organized to one side of a vertical line. To one side of the vertical line we record the last digit for every thing in rank request. Each line in the show is alluded to as a stem . Every digit on a stem is a leaf . 8 5 7 9 3 6 7 8

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Stem-and-Leaf Display Leaf Units A solitary digit is utilized to characterize each leaf. In the former illustration, the leaf unit was 1. Leaf units might be 100, 10, 1, 0.1, et cetera. Where the leaf unit is not appeared, it is expected to equivalent 1.

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Example: Leaf Unit = 0.1 If we have information with qualities, for example, 8.6 11.7 9.4 9.1 10.2 11.0 8.8 a stem-and-leaf show of these information will be Leaf Unit = 0.1 8 6 8 9 1 4 10 2 11 0 7

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Example: Leaf Unit = 10 If we have information with va