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Histograms & Summary Data

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  1. Histograms & Summary Data

  2. Histograms & Summary Data • Summarizing large of amounts of data in two ways: • Histograms: graphs give a pictorial representation of the data • Numerical summaries: gives snapshot of the data overall: • “Average”, “Mode”, “Median”, etc

  3. Histograms & Summary Data • Microsoft Excel has several tools that allows to summarize data: • sorting • Maximum • Minimum • range (difference between max and min) • mean (average) • grouping data • plotting a histogram

  4. Histograms & Summary Data • Sorting in Excel Click on “Data” Click on “Sort”

  5. Histograms & Summary Data • Sorting in Excel Store the data to be sorted in a list by columns Click to sort the column from low to high and vice versa Click “OK”

  6. Histograms & Summary Data • Sorting in Excel • Ex: On the class webpage, go to the file NBAPlayerHeights.xls • File contains data for the top ten player heights (in inches) by team during the 1990-91 season

  7. Histograms & Summary Data • Use the Sort tool in Excel to list all the player heights from smallest to largest First, highlight the data you wish to sort Go to “Data” and click “Sort” Click “Ascending”, then click “OK”

  8. Histograms & Summary Data • What is the smallest height? • Answer: 67 inches • What is the largest height? • Answer: 91 inches

  9. Histograms & Summary Data • MIN and MAX functions find the minimum value(s) and maximum value(s) in a list • The range is the maximum minus the minimum • AVERAGE function finds the average or mean • SUM function adds numbers in a list

  10. Histograms & Summary Data • Excel also has a Histogram tool • This function separates data into bins • The function counts how much data lies within each bin • You can (and should) define the size of the bin prior to opening the function

  11. Histograms & Summary Data • A histogram organizes data into groups by counting how much data is in each group • The groups are sometimes called “bins” • The number of observations in each “bin” is called the frequency

  12. Histograms & Summary Data • Installing the Histogram feature: Click on “Tools” and then on “Add-Ins”

  13. Histograms & Summary Data • Installing the Histogram feature: Click on these boxes Hit “OK” to install. It will take a few moments for these packs to install

  14. Histograms & Summary Data • Creating a Histogram Click on “Tools” Click “Data Analysis”

  15. Histograms & Summary Data • Creating a Histogram Click on “Histogram” Click “OK”

  16. Histograms & Summary Data • Creating a Histogram: Cells where your data is stored goes here Your Bin Limits or Bin Widths go here. You need to type these beforehand in your worksheet Choose the cell you want the frequencies of your bins to be displayed in Excel

  17. Histograms & Summary Data • Using NBAPlayerHeights.xls, create a histogram with bin widths of 5 starting at 65 inches

  18. Histograms & Summary Data • Create Bin Limits in Excel Create a cell called “Bin Limits” Enter your Bin Limits. Since we want bin to be width 5 there is only a difference of 5 between consecutive cells.

  19. Histograms & Summary Data Cell Range of Data Goes Here • Create Histogram Bin range you created goes here The cell where you want the frequencies to be displayed

  20. Histograms & Summary Data • And the Results . . . This number counts the number of times that player heights were greater than 65 but less than or equal to 70 inches

  21. Histograms & Summary Data • Plotting Our Results: • Click on Chart Wizard

  22. Histograms & Summary Data • Select Chart Type Click “Column”

  23. Histograms & Summary Data • Plotting Choose “Columns” Cell Range of your Histograms Frequencies goes here Click “Next”

  24. Histograms & Summary Data • Plotting: Click on “Series” tab from previous slide Type in the Cell Range of the Bin Limits your created Click on “Finish”

  25. Histograms & Summary Data • And the results:

  26. Histograms & Summary Data • Ex. Consider Excel file Sick Time.xls Find the mean, max, min, and range of hours at the Central plant. • Soln. Mean: 25.21 hours Min: 0 hours Max: 137 hours Range: 137 hours (max – min)

  27. Histograms & Summary Data • Ex. Construct a histogram of data with bin sizes of 10 hours. Construct another histogram of data with bin sizes of 8 hours.

  28. Histograms & Summary Data • Soln.

  29. Histograms & Summary Data • Soln.

  30. Histograms & Summary Data • Focus on the Project • In the sheet Data of Queue data.xls we see that the Friday 9 a.m. has more people that all other days at 9 a.m. • There is historical data for 5 weeks

  31. Histograms & Summary Data • Focus on the Project • A summary of the 9 a.m. data is given in the Excel file COUNTIF MIN AVERAGE MAX MAX - MIN

  32. Histograms & Summary Data • Focus on the Project • Since there are 573 customers in the 5 hours of data, this gives us customers per hour • For 60 minutes in an hour, this means that there are approx. 0.5236 minutes between arrivals

  33. Histograms & Summary Data • Focus on the Project • Create a histogram of the data, using appropriate bin limits (around 0.2 to 0.3 minutes for bin width)

  34. Histograms & Summary Data • Focus on the Project • From the histogram, we see that almost half of all the times between arrivals is less than 0.3 minutes

  35. Histograms & Summary Data • Focus on the Project • A summary of the 9 p.m. data is given in the Excel file COUNTIF MIN AVERAGE MAX MAX - MIN

  36. Histograms & Summary Data • Focus on the Project • Since there are 149 customers in the 5 hours of data, this gives us customers per hour • For 60 minutes in an hour, this means that there are approx. 2.0134 minutes between arrivals

  37. Histograms & Summary Data • Focus on the Project • Create a histogram of the data, using appropriate bin limits (around 1 minute for bin width)

  38. Histograms & Summary Data • Focus on the Project • Now that we know arrival time, we shift focus to service times • Service times do not depend upon time of day nor day of week

  39. Histograms & Summary Data • Focus on the Project • Service times for a single week are given in the file Queue Data.xls • There are 7634 service time records • Create histogram of these records

  40. Histograms & Summary Data • Focus on the Project • Bin size used – around 0.20

  41. Histograms & Summary Data • Focus on the Project • [9 a.m.] • Mean (average) arrival time is 0.52 minutes • Mean (average) service time is 1.21 minutes • Therefore, 1 ATM is probably not enough (using ONLY the mean times)

  42. Histograms & Summary Data • Focus on the Project • [9 a.m.] • If two ATMs were available for two customers, it would take 1.21 minutes • The service time would then be 0.605 • Therefore, 2 ATMs are probably not enough (using ONLY the mean times)

  43. Histograms & Summary Data • Focus on the Project • [9 a.m.] • By similar reasoning, 3 ATMs should be adequate (Note: 1.21/3 = 0.403 minutes per customer) • [9 p.m.] • 1 ATM would probably be adequate

  44. Histograms & Summary Data • Focus on the Project – What you should do: • Analyze the team data (number, min, mean, max, and range) • Create histograms for 9 a.m. and 9 p.m. arrival times • Create histogram for service times

  45. Histograms & Summary Data • Focus on the Project – What you should do: • Form preliminary estimates for the number of ATMs required for each of the two hours (9 a.m. and 9 p.m.)