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Problem 47 Hard Difficulty

When Russian billionaire Roman Abramovich became governor of the Russian province Chukotka (in the Bering Straits, opposite Alaska), it instantly became the fourth most prosperous region in Russia, even though its 80,000 other residents are poor. Mr. Abramovich was then worth $\$ 5.7$ billion. Suppose each of the $80,000$ other residents of Chukotka was worth $\$ 100 .$ Source: National Public Radio.
a. Calculate the average worth of a citizen of Chukotka.
b. What does this example tell you about the use of the mean to describe an average?


a. $\$ 71,349$
b. This result illustrates how the mean is susceptible to extreme data.
(Without Abramovich, the mean worth would have been $\$ 100$ )


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Video Transcript

this question tells the story of a billionaire moving to a very poor region of Russia and how that effects the mean value of this area. So essentially, what we have first, this this Teoh question is given in the form of frequency table. At first we have, um there are some people valued at $100. That's their value. Their X and their frequency, we're told, is 80,000 there, 80,000 of them valued at $100. Now Roman, aber Hema vich comes in at 5.7 $1,000,000,000. Now there's only one of him, but he's got a lot. Remember when we're using a frequency table to find, uh, on average, we know that X bar is equal to the sum of X times F over some of all the frequencies. So let's make another column for the X Times. The EFS will get that 100 times. Eight uh, 80,000 is eight million and one, Of course, one times 5.7 billion is just 5.7 billion. And now let's try to Sunday's up. When we add 80,000 and one will just be left with 80,000 and one and now when we add this is a little tricky will have to expand it out. What we get is 5.708 billion. So exporters equal to 5.708 billion over 8000, 80,000 and one. When we divide this out, we find that the mean value for each family living in this region is went from $100 to $71,349 and that's your final in.