1) Calculate the mean center and estimate the Euclidean median (to the nearest tenth) for the following sets of data.

{You can arrive at an estimate of the Euclidean mean using a simple spread sheet formula. I suggest using three columns (a, b, c) of a spread sheet (for example Excel). The first two columns will be designated for your estimates and the given x, y coordinates for each data point. Leave the first row blank, and then enter the x values in column A and y values in column B. In the first row of column C enter the following (or similar depending on spread sheet used – you may copy and paste the this formula into Excel if you like…be sure to include everything from the “=” to the final “)” but not the “.” at the end of the sentence!): =SQRT(((A2-A1)^2)+((B2-B1)^2))+ SQRT(((A3-A1)^2)+((B3-B1)^2))+ SQRT(((A4-A1)^2)+((B4-B1)^2))+ SQRT(((A5-A1)^2)+((B5-B1)^2))+ SQRT(((A6-A1)^2)+((B6-B1)^2)). Now enter your initial estimate of the Euclidean mean – x coordinate in the first row of column A, y coordinate in column B. Adjust each value up and/or down by tenths until you no longer get lower values in column C. You can start with either x or y, but be sure to return to adjusting the other any time to establish a new value for one!}

A) Once you have calculated the mean center and the Euclidean median for the above data, compare the graphic representation below. Does the change in the final data point affect the mean center or the Euclidean mean more? Can you explain the difference?

B) Calculate the standard distance for the above sets of data. How do the values compare? If you were to draw a circle centered at the mean center with a radius equal to the standard distance, how many data points would be included within or on the circle.

C) Calculate the relative distance for each data set and compare your results. How did you select an area for the calculation with each data set?

2) The following figures represent the location and size (age) of a single tree species on the edge of a grassland as seen from above, that is the strange bumpy globs are meant to represent each tree canopy. (The grassland is located to the south, or below the trees in the diagram.) The bottom diagram represents the same area as the top diagram following a five year interval. How might you use a weighted mean center to help determine if the tree species has encroached on the grassland during the five years? (Remember, when attributing weights to the differently aged trees, that younger (smaller) trees indicate more recent location of trees. I have provided a grid to help with location of trees [assume that they are located in the approximate center of each tree canopy depicted in the diagram].) What additional information would help you decide if the difference between the two figures is significant?