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F&W Chapter 10 questions, page 238-239
Here are the answers that I believe are correct. If you disagree, either review the relevant material in chapter 10 or let me know why you disagree.
1a. Mode
1b. Median
1c. Mean.
2a. Positive, but not more than about .5 or so.
2b. Positive, but somewhat less than a.
2c. Positive and pretty high. Slightly negative.
2d. Negative.
2e. Positive.
3. 1 - c
2 -d
3 – a
4 – b
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No. If the range is 0, the standard deviation will be zero. If the range is > 0, the way to make the standard deviation the largest is to have all the samples be on either the bottom of the range or on the top, with half on each side. Anything else will leave the range the same, but reduce the standard deviation. So, normalize the data so that the mean is zero. Make the distance from the mean to the top value d. Then the range will be 2d. The standard deviation will be sqrt( (d**2 + d**2)/2), or d. So, the range will always be at least twice the standard deviation.
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Yes. Add a constant to each value. Yes. Divide each value by 2.
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No. It tells us that the value is possible. So, any theory that predicts that this value will not be possible is disproved by counterexample.
11. 84%. 2.5%.
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