Exercise 3: 1. Recall the Chebyshev' rule. 2. Given the following data sets. The sample mean and sample standard deviation are as follows: 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.
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Exercise 3:
1. Recall the Chebyshev' rule.
2. Given the following data sets.
Data Set I
41
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
i = 50.0
s = 14.2
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.
C3
oull lia SI p
ENG
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