For this part of the assignment we were tasked with analyzing a sample of test scores from the Eau Claire School District. There was some worry from the public that the test scores were significantly lower at North High School than they were at Eau Claire Memorial and that firing teachers at North might be an appropriate. The results are below.
Eau Claire North
Scores Eau
Claire Memorial Scores
153
|
160.9231
|
<-- Average
|
145
|
158.5385
|
<-- Average
|
120
|
164.5
|
<--Median
|
189
|
159.5
|
<--Median
|
180
|
170
|
<--Mode
|
198
|
120
|
<--Mode
|
194
|
83
|
<--Range
|
140
|
91
|
<--Range
|
182
|
23.63544
|
<-- Standard Deviation
|
135
|
27.15766
|
<-- Standard Deviation
|
170
|
175
|
||||
175
|
182
|
||||
165
|
194
|
||||
164
|
107
|
||||
142
|
134
|
||||
130
|
165
|
||||
184
|
167
|
||||
170
|
120
|
||||
135
|
148
|
||||
188
|
189
|
||||
192
|
120
|
||||
120
|
190
|
||||
111
|
154
|
||||
170
|
120
|
||||
162
|
167
|
||||
154
|
175
|
||||
176
|
184
|
||||
145
|
145
|
||||
189
|
149
|
||||
164
|
193
|
||||
149
|
137
|
Using the given scores and Excel I was able to calculate a set of stats for each school including the range, mean, median, mode and standard deviation for each data set. The results show that even though an Eau Claire Memorial got the highest score (198) of the two schools it also achieved the lowest score too (107.) As a collective group the students at North outscored the Memorial students. The public could argue that North did better and the teachers should not have to worry for a couple of reasons. One, the mean or average test scores was two points higher than Memorial. Two, the median score for North is higher meaning the middle value of the given scores was better than Memorials (164 vs 159.) Next, North’s score range was less than Memorial’s showing the difference in the highest score and lowest score for the school was closer than Memorial’s highest and lowest score. Lastly, the standard deviation is lower for North showing their scores are more grouped together showing more group consistency. An argument that could be used against North is that Memorial had a higher top score (198 vs 194) and also had another student tie North’s top score. I think the best stat to illustrate this situation is the average score. The issue shouldn’t necessarily be about having a single student with a higher score but more focused on the overall group. North as a group achieved higher scores and was more consistent with their scores. Based on the information, the teachers at North should not be fired.
Part 2
For Part 2 of this assignment our job was to help an organic farming firm select where the best place to establish an organic goat farm was in Wisconsin. We were given very general information such as the number of goat and organic farms for each county but using statistics and creating some maps showing these stats, a decent well thought out recommendation should be able to be made.
The first step was using the data provided and calculate things such as the mean, median, mode, skewness, kurtosis and standard deviation for each data set. These will come in handy when creating the maps and interpreting the data later on.
| COUNTY | NAME | Organic Farms | Goat Farms |
| 001 | Adams | 1 | 12 |
| 003 | Ashland | 5 | 3 |
| 005 | Barron | 5 | 47 |
| 007 | Bayfield | 16 | 8 |
| 009 | Brown | 3 | 30 |
| 011 | Buffalo | 25 | 35 |
| 013 | Burnett | 6 | 11 |
| 015 | Calumet | 10 | 20 |
| 017 | Chippewa | 18 | 47 |
| 019 | Clark | 49 | 87 |
| 021 | Columbia | 15 | 49 |
| 023 | Crawford | 24 | 34 |
| 025 | Dane | 32 | 72 |
| 027 | Dodge | 20 | 57 |
| 029 | Door | 15 | 26 |
| 031 | Douglas | 5 | 18 |
| 033 | Dunn | 31 | 58 |
| 035 | Eau Claire | 27 | 44 |
| 037 | Florence | 0 | 9 |
| 039 | Fond Du Lac | 13 | 29 |
| 041 | Forest | 1 | 8 |
| 043 | Grant | 35 | 84 |
| 045 | Green | 16 | 81 |
| 047 | Green Lake | 2 | 25 |
| 049 | Iowa | 18 | 47 |
| 051 | Iron | 0 | 0 |
| 053 | Jackson | 23 | 41 |
| 055 | Jefferson | 9 | 43 |
| 057 | Juneau | 7 | 38 |
| 059 | Kenosha | 1 | 14 |
| 061 | Kewaunee | 2 | 17 |
| 063 | La Crosse | 26 | 22 |
| 065 | Lafayette | 24 | 35 |
| 067 | Langlade | 5 | 14 |
| 069 | Lincoln | 9 | 12 |
| 071 | Manitowoc | 21 | 36 |
| 073 | Marathon | 38 | 68 |
| 075 | Marinette | 4 | 15 |
| 077 | Marquette | 2 | 16 |
| 078 | Menominee | 0 | 0 |
| 079 | Milwaukee | 3 | 2 |
| 081 | Monroe | 59 | 74 |
| 083 | Oconto | 13 | 29 |
| 085 | Oneida | 3 | 7 |
| 087 | Outagamie | 11 | 35 |
| 089 | Ozaukee | 9 | 25 |
| 091 | Pepin | 5 | 9 |
| 093 | Pierce | 15 | 34 |
| 095 | Polk | 7 | 50 |
| 097 | Portage | 10 | 29 |
| 099 | Price | 4 | 12 |
| 101 | Racine | 5 | 33 |
| 103 | Richland | 28 | 34 |
| 105 | Rock | 18 | 59 |
| 107 | Rusk | 6 | 16 |
| 111 | Sauk | 38 | 74 |
| 113 | Sawyer | 4 | 5 |
| 115 | Shawano | 19 | 57 |
| 117 | Sheboygan | 6 | 54 |
| 109 | St. Croix | 18 | 57 |
| 119 | Taylor | 8 | 16 |
| 121 | Trempealeau | 32 | 31 |
| 123 | Vernon | 229 | 107 |
| 125 | Vilas | 0 | 5 |
| 127 | Walworth | 16 | 45 |
| 129 | Washburn | 3 | 20 |
| 131 | Washington | 12 | 31 |
| 133 | Waukesha | 1 | 21 |
| 135 | Waupaca | 5 | 36 |
| 137 | Waushara | 9 | 29 |
| 139 | Winnebago | 7 | 36 |
| 141 | Wood | 14 | 35 |
Using the information above here is the information I calculated using Excel.
| Organic Farms | Goat Farms | |
| Mean | 16.38888889 | 33.59722222 |
| Median | 9.5 | 31 |
| Mode | 5 | 35 |
| Skewness | 6.260257766 | 0.863929631 |
| Kurtosis | 46.54725042 | 0.538343524 |
| Standard Deviation | 28.0027556 | 23.04262941 |
| Sum | 1180 | 2419 |
Although having this information is wonderful it may be a hard to interpret visually in this format. Making maps using this data allows for a much more visually appealing way of presenting the data.
Three important stats to pay special attention to are Skewness, Kurtosis and Standard Deviation. Skewness is important because it shows how symmetrical the distribution is. The closer you are to zero the more symmetrical the data is. With this in mind if we look at the skewness of Organic Farms in Wisconsin we can see that at 6.26 there is a substantial difference between 6 and 0 in terms of skewness meaning our data is not very symmetrical. Looking at the Goat Farm data however presents a different story, with a skewness of .86 that is within the 1 to 0 threshold and means our data is distributed relatively symmetrically throughout. Kurtosis is important because it quantifies whether or not the data matches the Gaussian distribution. In order to have Gaussian Distribution the kurtosis has to be 0. Very similarly to skewness we see that the Organic Farm data is nowhere near to a Gaussian Distribution while the Goat Farm data is within the 1 threshold. Lastly standard deviation is important because it shows how closely data is clustered around the mean. By looking at the map above you can see the standard deviation for Goat Farms by county. The lower the standard deviation the more tightly your data is clustered around the mean.
Whether or not an Organic Goat Farm should be built in the state of Wisconsin really comes down to many variables. Some of the questions that need to be asked in addition to the data we were given include: What plants are you going to grow along with having the goats? Are you dedicating your sales to local markets? How big of farm do you want to have? Where is your primary customer base located? Do you want to be in an area that already has a lot of the same products you will have? Would you rather have the farm in an area with no other farms Organic or Goat related? These and many more questions need to be asked and considered when picking a location for a potential farm. Over 99% of Wisconsin farms are family owned, consumers are aware of this. The idea of an Ag Firm coming in might not sit as well with the consumers as they would hope.
Looking at the maps we can certainly see some patterns and they make sense knowing Wisconsin's topography and locations of large populations. Both Organic and Goat farms are located in the most popular agricultural counties around the state. Counties that have good soil, easily farmed terrain, climate although varies slightly throughout the state is certainly a factor, markets available in relation to the farms location. Based on the information I have, I would recommend Clark, Monroe, Vernon, Trempealeau, Grant counties all good possible candidates. These are counties with a rich history of agriculture and based on the data these counties all support a blend of Organic and Goat farms so having an Organic Goat Farm would be a perfectly acceptable. These counties are good for the firm if they are interested in taking other farms head on as there is obvious competition already established in these counties. As a wildcard county I would select Brown county. Although there is already a couple of Organic and Goat farms located in the county there is a huge opportunity for sales with Brown county being a huge tourism county. It is the home of Green Bay and also very close to the hugely popular Door county for visitors. If we had more information this area could be explored further but the potential is there simply based on the farm data. I believe the "Percentage of Organic Farms by County" and the "Percentage of Statewide Goat Farms Per County" are both great maps for explaining my reasoning.
The potential for a successful Organic Goat Farm in Wisconsin is certainly there. When doing a quick Google search for "wisconsin organic goat farm" there was more than 400,000 results. The interest and information is out there. There is pages of variables that need to be considered to make the most informed decision. A relatively safe bet for this farm would be one in a county already rich with agriculture and one to take a chance on would be one away from the most popular counties for farming but counties that really bank on tourism such as Brown or Door County, pending the right farming variables are there.
