HW1Solution

# HW1Solution - Geostatistics Petroleum and Geosystems...

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Geostatistics Petroleum and Geosystems Engineering 337 (19065) Spring 2008 Homework Assignment #1 From Page 23 1. True or False. For any list of numbers, half of them will be below the mean. ANSWER: FALSE. Consider a case where all of the numbers are clustered between 10 and 12, but one of the numbers is outside of this range and equals 10,000. Clearly, this one number will affect the mean, probably increasing it to above 12, which means most of the numbers would be below the mean. 2. Is the sample mean always the most frequently occurring value? If so, explain why. If not, give an example. ANSWER: NO. The answer from #1 also can be used here. In this case, the most frequently occurring number will be one of the numbers between 10 and 12. The sample mean will probably be out of this range, and there may have been no actual observations that equaled the mean. 3. Is the sample mean always equal to one of the values in the sample? If so, explain why. If not, give an example. ANSWER: NO. Consider a case where one observes only 3’s and 4’s. When the mean is computed, it will lie between 3 and 4, but will never equal 3 or 4 (unless of course a sample contains only 3’s or only 4’s). 4. Is the sample median always equal to one of the values in the sample? If so, explain why. If not, give an example. ANSWER: NO. When there are an odd number of observations in the sample, the median will equal the value in the middle of the sample. When there are an even number of observations, the median is defined as the average of the two central values. 5. Find a sample size for which the median will always equal one of the values in the sample. ANSWER: This will occur for all samples with an odd number of observations. 7. Is it possible for the standard deviation of a list of numbers to equal 0? If so, give an example. If not, explain why not. ANSWER: YES. The answer is yes. Remember that standard deviation is a measure of dispersion . What kind of list has no dispersion? Well, a list where all of the values are the same. You can examine the equation for variance and this should be obvious.

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## HW1Solution - Geostatistics Petroleum and Geosystems...

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