Contemplate the following data set (gerbils per cage):

A=10, B=15, C=13, D=16, E=12, F=13, G=13

1. For this data set, calculate (to two decimal places) the:

   
        a) Mean ________   b) Median ________   c) Mode ________
   
        d) Standard deviation        ________  
   
        e) Co-efficient of variation ________
   
        f) Skewness                  ________
   
   

   Contemplate the following map of the gerbil cages within your offspring's bedroom, while you wonder how s/he can stand the stench of cages and how you can stand your progeny's poor work ethic and sanitation standards:

   
               +----------------------+
               |     [b]         [e]  |
               |  [a]       [d]       |
               |       [c]            |
               |                      |
               |______                |            ^
               |      |        [f]    |            |  
               |      |               |            N
               |      |          [g]  |
               |      |               |       +---------+
               |      |            \          0         5 
               |      |             \             feet
               |      |              \ 
               +----------------------+
   
   

2. Using the orientation of the grid provided, calculate the (a) weighted mean center of the gerbil population and (b) the Manhattan median of the seven gerbil cages. Mark directly on the map and label each.

3. As a geographer living in Illinois, you've become rather personally interested in tornado occurrence. You've divided your general region into 9 quadrats 200 kilometers square. In each of these quadrats, you have determined that there is a 25 percent chance that a tornado will touch ground in the course of a year. What is the probability that 3 of the 9 quadrats will get hit with a tornado this year?

                                                       ________
   

4. On average, the police in a certain Midwestern college town are called to break up 3.1 noisy college parties somewhere in their jurisdiction during the school year.

   a) What is the chance that they will have a totally peaceful party weekend (i.e., no kegger complaints at all)?

                                                  ________
   

   b)What is the chance that there will be fewer complaints than average this weekend (less than or equal to 3 party pooping calls)?

                                                  ________
   

5. A biogeography product of the Chico State program, you have been employed as an ecologist in the U.S. Forest Service assigned to the San Bernardino National Forest. Among your excessive responsibilities, you have to monitor the feral burros in the Big Bear Lake area. You've come to know the local herds and even some individuals. In one particular herd of 15 jennies and 1 venerable jack, on average, 6 of the jennies foal, but there is some variability in this. The standard deviation is 3.1 foals over the twenty years that you and your predecessors have been monitoring this herd. Calculate the probabilities that:

   a) at least 80 percent of the jennies will foal this year

                                                       ________
   

   b) that fewer than 9 of them will deliver

                                                       ________
   

   So, now that you've convinced me that the last few weeks' work have not been deleted from your "hard drives," on to:

LAB EXERCISE B: Elements of Sampling and Spatial Sampling

For the next questions, read the appendices mentioned.

1. Contemplate the methodology statement in Appendix A of this exercise. What sort of sampling procedure was employed and why do you think the author chose this approach?

        _________________________________________________________________
   
        _________________________________________________________________
   
        _________________________________________________________________
   
        _________________________________________________________________
   
   

2. Continue your contemplation with Appendix B and do the same:

        _________________________________________________________________
   
        _________________________________________________________________
   
        _________________________________________________________________
   
        _________________________________________________________________
   
   

3. Do the same with Appendix C:

        _________________________________________________________________
   
        _________________________________________________________________
   
        _________________________________________________________________
   
        _________________________________________________________________
   

4. And Appendix D, while you're at it:

        _________________________________________________________________
   
        _________________________________________________________________
   
        _________________________________________________________________
   
        _________________________________________________________________
   
   

   The next questions get you up to speed on random number tables:

5. Design a routine you will use to pick numbers out of the table and describe it. Pick a starting point as randomly as you can, and then list the first 10 numbers, which conform to the following standard: they must be two digit numbers.

        _________________________________________________________________
   
        _________________________________________________________________
   
        _________________________________________________________________
   

6. Repeat the process, but this time select 10 numbers which conform to the following: three digit numbers with values between 200 and 799, inclusive.

        _________________________________________________________________
   
        _________________________________________________________________
   

7. Ditto once more, but this time select the first ten numbers that are even numbers one digit long.

        _________________________________________________________________
   
        _________________________________________________________________
   

   For the following experiments, you will need a copy of the current Butte County telephone directory.

8. Create the simplest and fastest statistically representative sample of 20 Butte County residents using the White Pages. List the folks' names and telephone numbers on a separate sheet of paper (numbered B- 8), together with a detailed and explicit description of just how you extracted these. What is this sampling strategy called?

9. Create a sample of 30 names and numbers from Butte, Sutter, Yuba, Nevada, and Sierra counties. Label this sheet B-9. This time, your list should be stratified proportionally by three strata: (1) Butte County; (2) Yuba-Sutter counties; and (3) Nevada and Sierra counties. Again, describe very precisely how you developed your list, and name that method.

10. Create a sample of 20 names and numbers, stratified non-proportionally, such that 10 of the names come from Butte County and 10 from Sutter-Yuba counties. Label this list B-10. Once more, describe how you extracted this list and name the procedure you followed.

11. On still another sheet of paper (B-11), use the Yellow Pages to extract a list of 20 business establishments and numbers, representing 10 different business types. These 10 business types should be taken from 10 randomly selected pages, with the business types taken also in a random fashion from the pages and the two names in each taken in a random fashion from the business types. Describe explicitly how you went about all this, including how you coped with anomalous situations, such as a page with nothing but one big ad on it or a business type with just one business listed. Now, which sampling procedure have you illustrated?

    The following questions deal with the basics of spatial sampling:

12. Select and mark 10 points on the following grid, using a simple random point sample method. The points must have whole integer X and Y coördinates. How'd you do it?

    
             0  1  2  3  4  5  6  7  8  9
          0  +--+--+--+--+--+--+--+--+--+
             |  |  |  |  |  |  |  |  |  |
          1  +--+--+--+--+--+--+--+--+--+
             |  |  |  |  |  |  |  |  |  |
          2  +--+--+--+--+--+--+--+--+--+
             |  |  |  |  |  |  |  |  |  | 
          3  +--+--+--+--+--+--+--+--+--+
             |  |  |  |  |  |  |  |  |  |  
          4  +--+--+--+--+--+--+--+--+--+  
    
    
         _________________________________________________________________
     
         _________________________________________________________________
    
         _________________________________________________________________
    
         _________________________________________________________________
    
    

13. Select and mark 25 points on the following grid, using a systematic point sampling strategy. Again, use integers, so that your points fall at the cross-points of the grid. Describe your strategy briefly.

    
              0 1 2 3 4 5 6 7 8 9
            0 +-+-+-+-+-+-+-+-+-+
            1 +-+-+-+-+-+-+-+-+-+
            2 +-+-+-+-+-+-+-+-+-+
            3 +-+-+-+-+-+-+-+-+-+
            4 +-+-+-+-+-+-+-+-+-+
            5 +-+-+-+-+-+-+-+-+-+
            6 +-+-+-+-+-+-+-+-+-+
            7 +-+-+-+-+-+-+-+-+-+
            8 +-+-+-+-+-+-+-+-+-+
            9 +-+-+-+-+-+-+-+-+-+
    
    
         _________________________________________________________________
    
         _________________________________________________________________
    
         _________________________________________________________________
    
         _________________________________________________________________
    

14. On the following grid of 100 quadrats, each 10 m on a side, select 10 using a simple random sampling method. There's an easy way and a more aggravating way to do this (and a bonus point goes to those who figure out the less aggravating way to handle this). Briefly describe that method.

                                            
              +--+--+--+--+--+--+--+--+--+--+
           10 |  |  |  |  |  |  |  |  |  |  |  
              |--+--+--+--+--+--+--+--+--+--|   
            9 |  |  |  |  |  |  |  |  |  |  |  
              |--+--+--+--+--+--+--+--+--+--|             
            8 |  |  |  |  |  |  |  |  |  |  |
              |--+--+--+--+--+--+--+--+--+--|             
            7 |  |  |  |  |  |  |  |  |  |  |  
              |--+--+--+--+--+--+--+--+--+--|             
            6 |  |  |  |  |  |  |  |  |  |  |  
              |--+--+--+--+--+--+--+--+--+--|             
            5 |  |  |  |  |  |  |  |  |  |  |  
              |--+--+--+--+--+--+--+--+--+--|             
            4 |  |  |  |  |  |  |  |  |  |  |  
              |--+--+--+--+--+--+--+--+--+--|             
            3 |  |  |  |  |  |  |  |  |  |  |  
              |--+--+--+--+--+--+--+--+--+--|             
            2 |  |  |  |  |  |  |  |  |  |  |  
              |--+--+--+--+--+--+--+--+--+--|             
            1 |  |  |  |  |  |  |  |  |  |  |  
              +--+--+--+--+--+--+--+--+--+--+
                1  2  3  4  5  6  7  8  9 10
    
    
         _________________________________________________________________
    
         _________________________________________________________________
    
         _________________________________________________________________
    
         _________________________________________________________________
    
    

15. There you are, a lone biogeographer out in the middle of the Tikaboo Valley of Nevada (nowhere is a local call), wondering whatever got you interested in desert vegetation. You have come here to set up transects along which you plan to pick points, identify the nearest big sagebrush plant (Artemisia tridentata) within 5 m of those points and, if there's one present, its nearest neighbor greater than 25 cm in height. So, pick an initial starting point for your first transect, using a simple random point sample method. Now, pick an orientation for your first transect, using 360 degrees of a circle (0 being true north) and a random number table. Draw a line with that orientation starting from the selected starting point on the map below. The line should be 5 km long. Now, repeat the process two more times, for a grand total of three transects.

    
         Bald                 Tikaboo Valley
          Mt.
                    0                10               20  km
                  0 +----------------------------------+      
                    |                                  |    Pahranagat     
                  2 |-                                -|         Range
                    |                                  |
                  4 |-                                -|
                    |                                  |           
                  6 |-                                -|         
                    |                                  |
                  8 |-                                -|  Tikaboo
                    |                                  |   Valey
                 10 |-                                -|
                    |                                  |
                 12 |-                                -|
                    |                                  |
                 14 |-                                -|
                    |                                  |
                 16 |-                                -|
                    |                                  |
     Jumbled     18 |-                                -|
       Hills        |                                  |
                 20 +----------------------------------+
                 km
    
    
    

LAB 5 APPENDIX A

Data

Roseman's ideas are rather difficult to implement. Since his theory generalizes from the behavior of individual migrant households to aggregate-level phenomena, any evaluation of that theory's validity should ideally make use of household-level data. The acquisition of such data is costly in terms of time and effort, as they must be obtained from the migrants: traditional data sources, such as the Census, are simply not available in the form that is the most appropriate to the Roseman framework. In order to obtain such household-level data, individual households belonging to the defined population of migrants must be specified.

In order to identify those households, the names and addresses of all parties purchasing properties in Northridge were obtained from the Los Angeles County Tax Assessor's Office. To distinuish migrant households from those parties purchasing homes, commercial properties, or residential properties for investment purposes, all names of companies and corporations were excluded as were family trusts buying multiple properties or those whose mailing addresses were different from the in situ addresses. After removing these elements, the remaining 1625 names were assumed to be those of migrant households.

The obtained sample of migrant households. -- The 325 households chosen comprised a twenty percent systematic random sample of the population described. The sample was drawn by arranging all the tax districts of Northridge in ascending numerical order, the names within each district remaining in the same order as found in the Tax Assessor's printouts. Then, every fifth name (after an initially randomly chosen starting point among the first five names) was taken for inclusion in the sample for a total of 325.

LAB 5 APPENDIX B

Unfortunately for this study, no comprehensive listing of archaeological sites exists on the global scale or on the regional scale needed here. There are no computer codings of "adequately known" archaeological sites to match the work of Erika Bouguignon and Lenora S. Greenbaum in ethnography or the George Peter Murdock Ethnographic Atlas on which their coding is based.

To provide an adequate sample, a list of all Near Eastern sites mentioned in some twenty secondary works on archaeology in the area was assembled. Presumably, a list assembled from secondary sources is composed of relatively well published sites. A workable sample of sites was drawn in a statistically unbiased way for more detailed data collection.

The list contains the alphabetized names of 536 Upper Palaeolithic through Neolithic/Chalcolithic sites in the Near East, ranging from 20,000 through 5,000 BP. Together with their names, locations and general technological level(s) have been coded. Forty-two sites were identified as Upper Palaeolithic in technological level, 87 as Epi-Palaeolithic, 63 as Mesolithic, and 408 as Neolithic. Neolithic takes in aceramic and ceramic Neolithic and Chalcolithic sites. These were not distinguished, because it proved impossible to identify the specific Neolithic level a priori. The four numbers add up to 600, rather than 536, because each major technological level within a site was counted as a separate occupation or settlement. Some sites were counted more than once, because they were occupied continuously or were reoccupied after a major change in technological level.

Once the sites were categorized as Upper Palaeolithic, Epi-Palaeolithic, Mesolithic, or Neolithic, a random sample of 60 was drawn. The sample is ten percent of the population of 600. The sample was stratified by general technological level, which corresponds roughly to the changing human relationship with nature that shapes the development of animal husbandry motives. Seven percent of the population were Upper Palaeolithic in character. Fifteen percent were Epi-Palaeolithic; ten percent were Mesolithic; and 68 percent were Neolithic. The sample was drawn from a random number table, such that the proportion of each level in the sample duplicated that in the population. Proportionally stratified random sampling was used in order to employ the non-parametric statistical techniques appropriate to nominal data.

LAB 5 APPENDIX C

A multi-stage ... sample of interviewing locations is employed in this research. At the first stage, 150 counties are selected with probabilities proportionate to population. At the second stage, within each of the first stage counties, three Census block groups are selected, with probabilities of selection proportionate to population. At the third stage, two locations are selected within each Census block group or equivalent. These locations constitute Census blocks or spatial equivalents in rural areas.

At the block level, the interviewers are assigned starting points and paths to proceed around the block. They attempt to interview at all households in the block until that point where they have reached assigned quotas of men and women and people over and under age 45. Once all four quotas are met, the interviewer leaves the neighborhood.

LAB 5 APPENDIX D

Data were gathered through the use of a questionnaire submitted to 222 respondents. The results can be regarded as tentative, because the sample is biased, representing only those persons most accessible. Despite the bias present, however, an effort was made to include representatives of most socio-economic groups living or working in the San Fernando Valley.