Exercise 3: 1. Recall the Chebyshev' rule. 2. Given the following data sets. Set I 41 Data 44 45 47 47 48 51 53 58 66 Data Set II 20 37 48 48 49 50 53 61 64 70 The sample mean and sample standard...

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Extracted text: Exercise 3: 1. Recall the Chebyshev' rule. 2. Given the following data sets. Set I 41 Data 44 45 47 47 48 51 53 58 66 Data Set II 20 37 48 48 49 50 53 61 64 70 The sample mean and sample standard deviation are as follows: Data Set I Data Set II i = 50.0 s = 14.2 i = 50.0 %3D s = 7.4 a. Which data set has a larger variation? (justify your answer) b. Is Chebyshev' rule verified for these two data sets. (Justify your answer graphically). c. What can we conclude? 3. In 1903, K. Pearson and A. Lee published the paper "On the Laws of Inheritance in Man. I. Inheritance of Physical Characters" (Biometrika, Vol. 2, pp. 357–462). The article examined data on forearm length, in inches, for a sample of 140 men. The mean and standard deviation of the forearm lengths are 18.8 in. and 1.12 in., respectively. a. Apply Chebyshev’s rule with k = 2 to make pertinent statements about the forearm lengths of the men in the sample. b. Repeat part (a) with k = 3.