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# Grouping and Displaying Data to Convey Meaning: Tables & Graphs chapter_2 _from_Statistics For Management

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This presentation is about Grouping and Displaying Data to Convey Meaning: Tables and Graphs
Contents were taken from Statistics for Management by Levin & Rubin.
Presentation includes,
How can we Arrange Data?
Raw Data
Arranging Data using Data Array & Frequency Distribution
Constructing a Frequency Distribution
Graphing Frequency Distributions
It also covers some solved examples of it.

Published in: Engineering, Technology, Business
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### Grouping and Displaying Data to Convey Meaning: Tables & Graphs chapter_2 _from_Statistics For Management

1. 1. Product Categories Per Customer at the PB Store
2. 2. September 11, 2001, attack on the World Trade Center in New York City and the Pentagon in Washington D.C. A Sad Day
3. 3. Grouping and Displaying Data to Convey Meaning: Tables and Graphs By Prof. P. N. Borkar (Asst. Prof. GHRCE, Nagpur)
4. 4. Some Definitions  Data: are collections of any number of related observations.  Data set: Collection of data.  Data point: single observation.
5. 5. Raw Data Arranging Data using Data Array & Frequency Distribution Constructing a Frequency Distribution Graphing Frequency Distributions How can we Arrange Data?
6. 6. How can we Arrange Data? Raw Data Arranging Data using Data Array & Frequency Distribution Constructing a Frequency Distribution Graphing Frequency Distributions
7. 7. How can we Arrange Data?  Aim: logical conclusion  Our observations must be organized so that we can pick out patterns Collecting Data:  Data came from actual observations or from records.  Computer programmers says ‘GIGO’
8. 8. … Test the data by asking questions:  Where did the data come from?  Do the data support or contradict other evidence?  Is evidence missing?  How many observations do we have?  Is the conclusion logical?
9. 9. … Difference between Samples & Populations  Population is a whole  Sample is fraction or segment of that whole  Information from sample makes inference about the population.  Ex. Poll of 2500 Indians to predict all adults living in India.
10. 10. … Advantages of samples,  Studying samples is easier  It costs less  Takes less time  Reduces risk ‘A representative sample contains relevant characteristics of population in the same proportion as they are included in that population’
11. 11. Exercise 1: Is this conclusion drawn from sample or population Q. 25% of cars sold in India in 2013 were manufactured in Japan. Ans: Population Reason: our department of commerce keeps statistics of all the cars sold in India
12. 12. How can we Arrange Data? Raw Data Arranging Data using Data Array & Frequency Distribution Constructing a Frequency Distribution Graphing Frequency Distributions
13. 13. Raw Data  Information before it is arranged & analyzed is called raw data. H.S CLG H.S CLG H.S CLG H.S CLG 3.6 2.5 3.5 3.6 3.4 3.6 2.2 2.8 2.6 2.7 3.5 3.8 2.9 3.0 3.4 3.4 2.7 2.2 2.2 3.5 3.9 4.0 3.6 3.0 3.7 3.2 3.9 3.7 3.2 3.5 2.6 1.9 4.0 3.8 4.0 3.9 3.1 2.5 2.4 3.2 Problem facing admission staff Data are not necessarily information. Goal: Summarize and present data in useful ways to support prompt and effective decisions.
14. 14. Exercise II: Look table of HS & CLG grades Q. Why do these data need further processing? Can you form any conclusion? Ans: we can not draw any conclusion form it. Need to: do certain amount of rearranging. (ex. Listing, grades from highest to lowest,
15. 15. How can we Arrange Data? Raw Data Arranging Data using Data Array & Frequency Distribution Constructing a Frequency Distribution Graphing Frequency Distributions
16. 16. Arranging Data using Data Array & Frequency Distribution  Data Array: arranges values in ascending or descending order. 16. 2 15. 8 15. 8 15. 8 16. 3 15. 6 15. 7 16. 0 16. 2 16. 1 16. 8 16. 0 16. 4 15. 2 15. 9 15. 9 15. 9 16. 8 15. 4 15. 7 15. 9 16. 0 16. 3 16. 0 16. 4 16. 6 15. 6 15. 6 16. 9 16. 3 Ex. Sample of Daily production in yards of 30 carpet looms 15. 2 15. 7 15. 9 16. 0 16. 2 16. 4 15. 4 15. 7 15. 9 16. 0 16. 3 16. 6 15. 6 15. 8 15. 9 16. 0 16. 3 16. 8 15. 15. 15. 16. 16. 16. Data Array
17. 17. … a better way The Frequency Distribution: Is a table that organizes data into classes Ex. Data Array of average inventory (in days) 2.0 3.8 4.1 4.7 5.5 3.4 4.0 4.2 4.8 5.5 3.4 4.1 4.3 4.9 5.5 3.8 4.1 4.7 4.9 5.5 Class Frequency 2.0 to 2.5 1 2.6 to 3.1 0 3.2 to 3.7 2 3.8 to 4.3 8 4.4 to 4.9 5 5.0 to 5.5 4 Frequency Distribution Note: we lose some information in constructing frequency distribution, yet it offers new insights into patterns of data.
18. 18. … Relative Frequency Distribution: - It express the frequency of each value as a fraction or a percentage of total number of observations. Class Frequency Relative Frequency 2.0 to 2.5 1 0.05 2.6 to 3.1 0 0.00 3.2 to 3.7 2 0.10 3.8 to 4.3 8 0.40 4.4 to 4.9 5 0.25 5.0 to 5.5 4 0.20 20 1.00
19. 19. Exercise III: Data array and frequency distribution 823 648 321 634 752 669 427 555 904 586 722 360 468 847 641 217 588 349 308 766 Company: PB Transmission Fix-It Number of service tickets submitted by 20 stores Q. How many stores are not breaking even and how many are to get bonus ? Not breaking even < 475 To get bonus > 725 217 360 586 648 766 308 427 588 669 823 321 468 634 722 847 349 555 641 752 904 Not breaking even : 7 To get bonus : 5
20. 20. … 4.3 2.7 3.8 2.2 3.4 3.1 4.5 2.6 5.5 3.2 6.6 2.0 4.4 2.1 3.3 6.3 6.7 5.9 4.1 3.7 Company: PB Transmission Fix-It Number of hrs taken by mechanics to remove, repair and replace transmissions Q. Construct frequency distribution with intervals of 1.0 hrs ? What conclusions can you reach about productivity of mechanics ? If more than 6.0 hrs is evidence of unsatisfactory performance, does it have major or minor problem with particular store? Class 2.0 to 2.9 3.0 to 3.9 4.0 to 4.9 5.0 to 4.9 5.0 to 6.9 Frequenc y 5 6 4 2 3 2 2.7 3.4 4.3 5.9 2.1 3.1 3.7 4.4 6.3 2.2 3.2 3.8 4.5 6.6 2.6 3.3 4.1 5.5 6.7 There is only 15 % takes more than 6 hrs, it is minor productivity problem
21. 21. How can we Arrange Data? Raw Data Arranging Data using Data Array & Frequency Distribution Constructing a Frequency Distribution Graphing Frequency Distributions
22. 22. Constructing a Frequency Distribution 16. 2 15. 8 15. 8 15. 8 16. 3 15. 6 15. 7 16. 0 16. 2 16. 1 16. 8 16. 0 16. 4 15. 2 15. 9 15. 9 15. 9 16. 8 15. 4 15. 7 15. 9 16. 0 16. 3 16. 0 16. 4 16. 6 15. 6 15. 6 16. 9 16. 3 Ex. Sample of Daily production in yards of 30 carpet looms Step 1: Decide on the type and number of classes for dividing the data Need to consider Attributes, here we have considered yards produced. How many number of classes ? What will be the range of each class ?
23. 23. … Class in Yards Frequency 15.1 to 15.5 2 15.6 to 16.0 16 16.1 to 16.5 8 16.6 to 17.0 4 30 Class in Yards Width Frequency 15.1 to 15.5 0.5 2 15.6 to 15.8 0.3 8 15.9 to 16.1 0.3 9 16.2 to 16.5 0.4 7 16.6 to 16.9 0.4 4 30 Equal Width Unequal Width Problem with unequal width: distribution is much more difficult to interpret.
24. 24. … So we need to make the class intervals of equal size, Width of class interval = Next unit value after largest value Smallest value in the data- Total Number of class intervals = (17.0 – 15.2)/ 6 = 0.3 Yards
25. 25. … Step 1I: Sort the data points into classes and count the number of points in each class Class in Yards Frequenc y 15.2 to 15.4 2 15.5 to 15.7 5 15.8 to 16.0 11 16.1 to 16.3 6 16.4 to 16.6 3 16.7 to 16.9 3 30 15. 2 15. 7 15. 9 16. 0 16. 2 16. 4 15. 4 15. 7 15. 9 16. 0 16. 3 16. 6 15. 6 15. 8 15. 9 16. 0 16. 3 16. 8 15. 6 15. 8 15. 9 16. 1 16. 3 16. 8 15. 6 15. 8 16. 0 16. 2 16. 4 16. 9
26. 26. … Step III: Illustrate the data in a chart looms<-c(16.2, 15.7, 16.4, 15.4, 16.4, 15.8, 16.0, 15.2, 15.7, 16.6, 15.8, 16.2, 15.9, 15.9, 15.6, 15.8, 16.1, 15.9, 16.0, 15.6, 16.3, 16.8, 15.9, 16.3, 16.9, 15.6, 16.0, 16.8, 16.0, 16.3) breaks=seq(15.1, 17.0, 0.4) cbind(table(cut(looms, breaks))) hist(looms, breaks="Sturges")
27. 27. Exercise IV: Here are the ages of 30 people who bought video recorder @ PB Music Shop 26 37 40 18 14 45 32 68 31 37 20 32 15 27 46 44 62 58 30 42 22 26 44 41 34 55 50 63 29 22 Q. Looking data just as they are, what conclusions can you come to quickly about PB Music shop? Ans: It is difficult to tell anything from raw data
28. 28. … Q. Construct a 6 category closed classification. Does having this enable you to conclude anything more about PB Music shop ? Class 10-19 20-29 30-39 40-49 50-59 60-69 Frequenc y 3 7 7 7 3 3 Most video recorders are bought by people between 20 to 50, so marketing effort should be aimed at that group
29. 29. How can we Arrange Data? Raw Data Arranging Data using Data Array & Frequency Distribution Constructing a Frequency Distribution Graphing Frequency Distributions
30. 30. Graphing Frequency Distributions Graph gives data in two-dimensional picture. Horizontal Axis: values of variable Vertical Axis: frequencies of the classes Histograms: Is series of rectangles, each proportional in range of values and proportional in number of items falling in it.
31. 31. … Frequency Polygons I: mark frequencies on vertical axis and values of variables on horizontal axis II: plot each class frequency by drawing dot above its midpoint, and connect the successive dots with straight lines
32. 32. … Why do we need both? Histogram 1. Rectangle clearly shows each separate class in the distribution. 2. The area of rectangle, shows proportion of the total number of observations that occur in class. Frequency Polygon 1. It is simpler 2. It sketches outline of the data pattern more clearly 3. Polygon becomes smooth and curvelike as we increase the number of classes and the number of
33. 33. … Ogives  Is a graph of cumulative frequency distribution.  It enables us to see how many observations lie above or below certain values.
34. 34. Exercise IV: Ganga River: River flow Frequenc y 1001-1050 7 1051-1100 21 1101-1150 32 1151-1200 49 1201-1250 58 1251-1300 41 1301-1350 27 1351-1400 11 Total 246 Q.1: Create More than Ogive River flow > Frequency Cumulative frequency 1000 7 246 1050 21 246-7=239 1100 32 239-21=218 1150 49 218-32=186 1200 58 186-49=137 1250 41 137-58=79 1300 27 79-41=38 1350 11 38-27=11 1400 0 11-11=0
35. 35.
36. 36. PB Store Product Categories Frequency Distribution At the Miami, Florida, airport, officials each week select a random sample of passengers. For each person selected, the time spent in the security screening line is recorded. The waiting times (already sorted from high to low), in seconds, for one such sample of 72 passengers are as follows: