Interhill data Distance (m) Paies to Snowland hill 945 Snowland hill to Irohir 1020 Irohir to 3rd hill 405 3rd hill to Nankapw 1385 Nankapw to 3rd hill 1385 3rd hill to Irohir 393 Irohir to Snowland hill 1035 Snowland to Paies 945 1 ratio Level of measure? 2 8 Find the sample size n for the interhill distance data. 3 393 Find the minimum interhill distance. 4 1385 Find the maximum interhill distance. 5 992 Find the range of the interhill distance. 6 982.5 Find the median interhill distance. 7 None Find the mode for the interhill distance. 8 939.13 Find the sample mean x interhill distance. 9 377.39 St dev 10 0.4019 Find the sample coefficient of variation CV. 11 248 Four bin width? 12. Bins (x) Frequency (f) Rel. Freq. p(x) 641 2 0.25 889 0 0 1137 4 0.5 1385 2 0.25 Sum: 8 1 13 RF histogram 14 bimodal What is the shape of the distribution? Bin Freq RF or p(x) x*p(x) 2 0 0 0 3 7 0.44 1.31 4 5 0.31 1.25 5 4 0.25 1.25 Sums: 16 1 3.81 15 3.81 What is the mean? 16 -0.0174 slope Interhill data Time (min) Speed (m/s) 17 3.0144 intercept Paies to Snowland hill 5.4 2.94 18 negative sign of corr Snowland hill to Irohir 11.4 2.79 19 -0.9849 correlation Irohir to 3rd hill 13.9 2.76 20 high degree of corr 3rd hill to Nankapw 23 2.56 21 linear linear? Nankapw to 3rd hill 32.1 2.52 22 0.9700 Coef Det 3rd hill to Irohir 34.8 2.46 23 97.00% Percent variation Irohir to Snowland hill 42.3 2.31 24 3.01 start speed at t=0 Snowland to Paies 49.9 2.08 25 1.97 speed at t=60 26 slowing down What is happening? 27 tiring/variable Why? Some answered "Why is he slowing down?" others answered "Why did I conclude he is slowing down?" Is the data non-linear? There is no obvious curve to the data: the trend line splits data left and right. The line appears to well match the data at the endpoints and the data at the midpoints. The data shows a runner continously slowing down. A residual analysis will help satisfy more statisically advanced readers. Time (min) Speed (m/s) Predicted Residuals Standard Err 5.4 2.94 2.92 0.02 0.0004 11.4 2.79 2.82 -0.03 0.0007 13.9 2.76 2.77 -0.01 0.0002 23 2.56 2.62 -0.06 0.0030 32.1 2.52 2.46 0.06 0.0040 34.8 2.46 2.41 0.05 0.0025 42.3 2.31 2.28 0.03 0.0009 49.9 2.08 2.15 -0.07 0.0046 0.0162