1. Numerical Methods for Describing Data
From Graphical to Numerical

2.   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.
…+122 13
Median = 133

3. 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.
Median = 189
Median = 189
The mean is nonresistant to outliers.
Trimmed mean = 191

4.    3.    The ages (measured by last birthday) of the employees of Dewey, Cheatum and Howe are listed below.
Median = 35.5 4H 4L 3H 3L 2H 2L
35.5 42 29 Q1
median Q3

5.  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.

6. Observations: Deviations: Squared deviations6
6 – 14.4
21 – 14.4 21 4
4 – 14.4 30
30 – 14.4 11
11 – 14.4

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