Assignment 2

Part 1

Definitions

• Range: is the difference between the highest and lowest values in a set of data
• Mean: is the average of the data found from dividing the sum of a data set by the total number of observations
• Mode: is the most common observation found in a  given data set
• Kurtosis: is the how much a set of data falls along the tails of its statistical distribution 
• Skewness: can be described as the tendency for a set of data to fall on either the positive or negative side of the mean for a given set of data
• Standard Deviation: is a way of describing how dispersed a set of data is

Eau Claire North's teach staff has begun to question their teaching style when comparing their Standardized Test scores to Eau Claire Memorial's test scores. The concern stems from the fact that Eau Claire Memorial has always had the highest single test score. Both of the schools Standardized Test scores are shown below (Figure 1). A statistical analysis of the two school's scores below aims to bring clarity to the question of Eau Claire North's test scores not being as good as Eau Claire Memorial.

Figure 1. The tested sample of Standardized Test Scores for both high schools

Test Score Statistics

• Eau Claire North
• Standard Deviation: 23.635
• Mean 160.923
• Median: 164.5
• Mode: 170
• Kurtosis: -0.557
• Skewness: -0.579
• Range: 74
• Eau Claire Memorial
• Standard Deviation: 27.157
• Mean: 158.539
• Median: 159.5
• Mode: 120
• Kurtosis: -1.174
• Skewness: -0.185
• Range: 91

Analysis

Based upon the statistics shown above Eau Claire North's teachers should not be worried about their test scores. When comparing the two schools, Eau Claire North has a smaller standard deviation than that of Eau Claire Memorial meaning that Eau Claire North's test scores are more consistent and differ from the mean less than Eau Claire Memorial. Eau Claire North also has a higher overall test score mean than that of Eau Claire Memorial. Also, when looking at the two data sets kurtosis, Eau Claire North's test scores Kurtosis is smaller than Eau Claire Memorial meaning fewer scores fall at the ends of the distribution. As a whole, the teachers at Eau Claire North should not be concerned about their test scores compared to Eau Claire Memorial. Eau Claire Memorial does have the highest single test score but their scores are more variable and dispersed than those of Eau Claire North meaning the teaching methods being employed at Eau Claire North produce better scores as a whole when more statistical analysis is applied to their respective samples.

Figure 2. The figure above shows the calculations used to find the Standard Deviation of the two schools test scores

Part 2: Mean Centers

Mean Centers are the calculation of is average x and y values of a given data set

The Map below (Figure 3) shows three different mean centers calculated for the state of Wisconsin. They are the geographic mean center, weighted mean center the population in 2000 and the weighted mean center for population in 2015. When looking at the map below (Figure 3.) a few patterns standout. Many populations in the Northern Counties have experienced a decline in their populations since 2015. Counties in the Northeast and Southeast have seen their populations increase with the largest increase in Dane County (blue county located in southern Wisconsin). These shifts in populations may be caused by an increase in economic productivity in the northeast and southern regions of the state leading people from northern counties to begin to move southward. 

The Geographic mean center is the center of Wisconsin calculated by the average county area. The weighted means are the geographic mean only weighted by the total population in each county. The weighted mean center for 2015 shifted slightly southwest from its location in 2000. This is mainly caused by the increases in population in the southern counties of Wisconsin with the largest pull coming from Dane County located southwest of the 2000 weighted mean center. 

Figure 3. Map displaying the Wisconsin County population changes between 2000 and 2015 as well as the Geographic Mean Center and both Weighted Mean Centers for 2000 and 2015