Assignment 2

Part 1: Cycle Fever

The TOUR de GEOGRAPHIA is fast approaching, and I've got the need for speed. Team ASTANA(TA) is the safe bet to invest in, constantly churning out race winners year after year; however, Team TOBLER(TT) has been quietly making a name for themselves. The following statistics will help to determine the choice to invest in this year.

Range

The range is the difference between the highest and lowest value of each sample size. The range for TA is one hour and ten minutes, while the range for TT is thirty minutes. This shows TA has a few outliers which cause the range to look inflated, while TT still remains as a pack with a relatively small range.

Mean

The mean is the sum of all values, divided by the number of records per sample. TA has a mean of thirty-seven hours and fifty seven minutes. TT has a mean of thirty-eight hours and five minutes. 

Median

The median is the middle point of the values. It has the same number of records higher than it, and lower than it. The median for TA is thirty-eight hours exactly, while TT's median is thirty-eight hours and nine minutes.

Mode

The mode is the value that is most often repeated in the data. TA's mode is thirty-eight hours, and TT's mode is thirty-eight hours and nine minutes.

Kurtosis

Kurtosis is the height comparison of the graph to the normal or gaussian curve. A negative kurtosis is a value less than 1. This means that the peak will be flatter than normal and the data is more spread out. A positive kurtosis is greater than one and means that the peak is higher than the normal and there are more observations closer to the mean. TA's kurtosis is 1.17, while TT's is 2.93.

Skewness

Skewness is the distribution of how the curve of a dataset compares to the normal symmetry. A value of zero means there is no skewness and the curve will look normal. A positive number means that the curve is skewed to the left of the normal curve. A negative number means that the curve is skewed to the right of a normal curve. TA's skewness is -.0026, and TT's skewness is -1.56.

Standard Deviation

Standard deviation is an attempt to discuss the distribution of how observations are clustered around the mean. A standard deviation below one says that the data falls within thirty-four percent of either side of the mean. A standard deviation below 2 describes the data within forty-seven and a half percent of either side of the mean. A standard deviation below 3 explains ninety-nine percent of all observations. TA's standard deviation is 17.49, and TT's is 7.78. (Work is below in figure 1).

Investing

Due to all of the stats, it appears that the teams will exhibit tendencies close to what was predicted. Team ASTANA will produce a relatively average team with a skewness close to zero and a kurtosis very close to one. The range suggests that they will have very low minimum times, indicating a possible individual winner. Team TOBLER will produce a team with a skewness of -1.56 suggesting that they will have a majority of values above the mean, with a high kurtosis to suggest that their values will be clustered around the mean. This would make me think that the team will have times higher than the mean, and will be clustered around there.

All of these statistics make me inclined to invest in Team ASTANA, as they appear to have very high performing individuals, and their team statistics suggest that their team performs better than Team TOBLER. These statistics make me think that I will get a higher return on both the individual winner and the team funds.

Figure 1: Hand work done on standard deviation.

Part 2: Wisconsin's Center

Figure 2: Map depicting geographic mean center, and weighted population centers of 2000 and 2015.

This map places the geographic mean center of the state in the center. It also places a population weighted center for the years of 2000 and 2015 on the map. One possible explanation for the movement of the weighted population center is the loss of population in the Madison, and Milwaukee areas. This would help to explain why the point moves NW from the cities in 2015 as they lost population weight.