Consider the three scenarios below: The business magazine Forbes estimates (Nove
ID: 3134677 • Letter: C
Question
Consider the three scenarios below:
The business magazine Forbes estimates (November 6, 1995) that the "average” household wealth of its readers is either about $800,000 or $2.2 million, depending on which "average” it reports. Which of these numbers is the mean wealth and which is the median wealth? Explain your answer.
Choose four numbers from the whole numbers 0 to 10, with repeats allowed, such that the four numbers will have the smallest possible standard deviation. Explain the reasoning behind your choice.
Choose four numbers from the whole numbers 0 to 10, with repeats allowed, such that the four numbers will have the largest possible standard deviation. Explain the reasoning behind your choice.
Explanation / Answer
The business magazine Forbes estimates (November 6, 1995) that the "average” household wealth of its readers is either about $800,000 or $2.2 million, depending on which "average” it reports. Which of these numbers is the mean wealth and which is the median wealth? Explain your answer.
As the mean is more influenced by outliers, and we can only expect high extreme value, then
MEDIAN: $800000
MEAN: $ 2.2 MILLION [ANSWER]
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Choose four numbers from the whole numbers 0 to 10, with repeats allowed, such that the four numbers will have the smallest possible standard deviation. Explain the reasoning behind your choice.
The smallest standard deviation is 0, which happens when all entries are identical. Hence, we can choose
{5,5,5,5} [ANSWER]
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Choose four numbers from the whole numbers 0 to 10, with repeats allowed, such that the four numbers will have the largest possible standard deviation. Explain the reasoning behind your choice.
Standard deviation grows bigger when the entries are far from the mean. Hence, we want the entries are far as possible from the mean, so we want the extremes,
{0,0,10,10} [ANSWER]
[To get a mean of 5, which is far from both 0 and 10.]