7.85 ● Measures of nerve conductivity are used in the diagnosis of certain medical conditions. The paper

“Effects of Age, Gender, Height, and Weight on Late Responses and Nerve Conduction Study Parameters”

(Acta Neurologica Taiwanica [2009]: 242–249) describes a study in which the ulnar nerve was stimulated in healthy patients and the amplitude and velocity of the response was measured.

Representative data (consistent with summary quantities and descriptions given in the paper) for 30 patients for the variable x 5 response velocity

(m/s) are given in the accompanying table. Also given are values of the log of x and the square root of x.

x log(x) sqrt(x)

60.1 1.78 7.75 48.7 1.69 6.98 51.7 1.71 7.19 52.9 1.72 7.27 50.5 1.70 7.11 58.5 1.77 7.65 53.6 1.73 7.32 60.3 1.78 7.77 64.5 1.81 8.03 50.4 1.70 7.10 56.5 1.75 7.52 55.5 1.74 7.45 53.0 1.72 7.28 50.5 1.70 7.11 54.0 1.73 7.35 53.6 1.73 7.32 55.2 1.74 7.43 57.9 1.76 7.61 61.5 1.79 7.84 58.0 1.76 7.62 57.6 1.76 7.59 67.1 1.83 8.19 56.2 1.75 7.50 53.8 1.73 7.33 55.7 1.75 7.46 52.9 1.72 7.27 54.0 1.73 7.35 52.6 1.72 7.25 61.8 1.79 7.86 62.8 1.80 7.92

a. Construct a histogram of the untransformed data.

b. Does the distribution of x appear to be approximately normal? Explain.

c. Construct a histogram of the log transformed data.

d. Is the histogram of the transformed data more symmetric than the histogram of the untransformed data?

e. Construct a histogram of the square root transformed data.

f. Do either of the two transformations (square root or log) result in a histogram that is more nearly normal in shape? (Hint: See Example 7.33.)