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# Aortic stenosis refers to a narrowing of the aortic valve

ISBN: 9780321629111 32

## Solution for problem 67E Chapter 1

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 67E

Aortic stenosis ?refers to a narrowing of the aortic valve in the heart. The paper “Correlation Analysis of Stenotic Aortic Valve Flow Patterns Using Phase Contrast MRI” (?Annals of Biomed. Engr?., 2005: 878–887) gave the following data on aortic root diameter (cm) and gender for a sample of patients having various degrees of aortic stenosis: a.?? ompare and contrast the diameter observations for the two genders. b. ?Calculate a 10% trimmed mean for each of the two samples, and compare to other measures of center (for the male sample, the interpolation method mentioned in Section 1.3 must be used).

Step-by-Step Solution:

Answer: Step 1 of 2 a. We need to compare and contrast the diameter observations for the two genders. Sl. No. M F 1 3.7 3.8 2 3.4 2.6 3 3.7 3.2 4 4 3 5 3.9 4.3 6 3.8 3.5 7 3.4 3.1 8 3.6 3.1 9 3.1 3.2 10 4 3 11 3.4 12 3.8 13 3.5 Mean 3.638462 3.28 Median 3.7 3.15 Standard 0.269377 0.477959 deviation Q1 3.4 3.025 Q2 3.7 3.15 Q3 3.8 3.425 IQR(Q3 - Q1) 0.4 0.4 From Excel function we use Mean “=average( )” Median “=Median( )” Stdev “=stdev( )” Q1 “=quartile(range, 1)” Q2 “=quartile(range, 2)” Q3 “=quartile(range, 3)” Here, Aortic root diameters for males are x = 3.64 cm, Median = 3.70 cm, standard deviation s = 0.269 cm, and fourth spread or Interquartile Range (IQR) = 0.40. Similarly, Aortic root diameters for females are x = 3.28 cm, Median = 3.15 cm, s = 0.478 cm, and fourth spread or Interquartile Range (IQR) = 0.50 cm. Aortic root diameters are typically smaller for females than for males, and females show more variability. The Graphical representation is given below. The distribution for males is negatively skewed, while the distribution for females is positively skewed.

Step 2 of 2

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