Numerical Methods for Describing Data From Graphical to Numerical

  1. Traumatic knee dislocation often requires surgery to repair ruptured ligaments. One measure of recovery is range of motion (measured by the angle formed when, starting with the leg straight, the knee is bent as far as possible). The article “Reconstruction of the Anterior and Posterior Cruciate Ligaments after Knee Dislocation” reported the following post surgical range of motion for a sample of 13 patients.   154 142 137 133 122 126 135 135 108 120 127 134 122 154+142+137+…+122 13 108 120 122 122 126 127 133 134 135 135 137 142 154 Median = 133

The mean is nonresistant to outliers. 2. The paper “The Pedaling Technique of Elite Endurance Cyclists” reported the accompanying data on single-leg power at a high workload. 160 174 176 180 180 183 187 191 194 200 205 211 211 244 Median = 189 160 174 176 180 180 183 187 191 194 200 204 205 211 211 Median = 189 The mean is nonresistant to outliers. Trimmed mean = 191

   3.    The ages (measured by last birthday) of the employees of Dewey, Cheatum and Howe are listed below. 22 31 21 49 26 42 42 30 28 31 39 39 20 37 32 36 35 33 45 47 49 38 28 48 Median = 35.5 9 2 2 5 7 9 8 1 0 1 9 9 7 2 6 5 3 8 2 2 1 6 8 0 8 4H 5 7 8 9 9 4L 2 2 3H 5 6 7 8 9 9 3L 0 1 1 2 3 2H 6 8 8 2L 0 1 2 35.5 42 29 20 21 22 26 28 28 30 31 31 32 33 35 36 37 38 39 39 42 42 45 47 48 49 49 Q1 median Q3

 4. In the Consumer’s Report October 2013 issue, a random sample of dishwasher detergents tested produces the following 5 values (price per load in cents)   Kirkland Signature Gel 6¢ Cascade Complete Powder 21¢ Sun Powder 4¢ Ecover Zero 30¢ Trader Joe’s Powder 11¢ Median = 11¢ Standard deviation (and variance) gives us a measure of how far a set of numbers is spread out.

Observations: Deviations: Squared deviations 6 6 – 14.4 21 – 14.4 21 4 4 – 14.4 30 30 – 14.4 11 11 – 14.4

Standard deviation With the Laundress variance Roughly speaking, the standard deviation of 10.92 ¢ measures a typical or average distance between the individual detergent prices and the mean detergent price. With the Laundress