ENGI 3423 Probability and Statistics

Faculty of Engineering and Applied Science
2010 Fall

Assignment

[Descriptive Statistics]

To be submitted no later than 10:00 on Wednesday 22 29 September, 2010.

The waiting time required to observe a second arrival in a queue is recorded on 64 occasions.   The 64 values are listed here:

         6.8664   56.0366   32.1577   31.2875   32.6379   17.5727
        50.2993   33.6218   80.7547   26.7776    9.7068   47.8096
         4.7442   20.7012   10.8955   19.6846   21.0011   27.1825
        37.5551   27.7152   69.6380   29.0106   44.5771   27.8161
        22.9777   50.0664   42.1960   14.5863   67.1175   17.8470
        42.1718   61.1624   52.3220   25.5739   16.7999   36.9206
        42.5967   13.0874   16.5333   45.7174   26.4462   10.3207
        38.8887   12.2077   33.7100   33.1783   35.8122   19.5911
        48.2173   54.8926   61.8550   56.5231   45.1284   26.3037
        17.3146   87.2031    6.9923   14.3766   29.2347   20.0414
        38.8940   41.8836   13.9692   17.5466

These data are also available as a plain text file from this link.

1. Create a printout of Minitab’s standard “Descriptive Statistics Graph” output (as was demonstrated in the Minitab tutorial), (or provide equivalent information from some other software package).
   Ensure that your list of descriptive statistics includes

   • the count (number of values), the mean, the standard deviation, the variance,
   • the least (minimum) value, the greatest (maximum) value and
   • all three quartiles (including the median).

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2. Generate a boxplot for these data, including the following features:
   

   • the box is oriented horizontally;
   • the box is coloured (not grey, white or black);
   • there is a line across the box for the location of the median;
   • there are whiskers (extending to the most extreme values between the inner fences);
   • there is a symbol for the location of the outlier;
   • there is a symbol for the location of the arithmetic mean;
   • there are gridlines at every ten minutes from 0 to 90 minutes; and
   • there is an appropriate title for the boxplot.

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3. Show your calculations to determine whether the outlier is mild or extreme.

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4. What evidence do you see in the boxplot for skewness in these data?

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5. Create a stem-and-leaf diagram for these data.
   Trim the outliers and set the increment to 10.

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6. Construct a histogram for these data, including the following features:
   

   • the horizontal axis runs from 0 to 90;
   • the first four bars span five minutes each
     (so that the second bar covers 5 to 10 minutes);
   • the next two bars span ten minutes each;
   • the seventh bar spans 40 to 60 minutes;
   • the final bar spans 60 to 90 minutes;
   • horizontal gridlines are present;
   • the axes have appropriate labels; and
   • there is an appropriate title for the histogram.

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7. Show the calculation to determine the frequency for the interval [15.0, 20.0) directly from the histogram.

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8. Comment on the presence of the one outlier.

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