When Russian billionaire Roman Abramovich became governor of...

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?

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?

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Key Concepts

Arithmetic Mean

The arithmetic mean is the sum of all individual values divided by the number of values. It is commonly used as a measure of central tendency to represent an overall 'average' value for a dataset. However, when a dataset includes extreme values or outliers, the arithmetic mean can be misleading because it gets skewed towards those extreme values.

Outlier Influence

Outliers are values that are significantly higher or lower than most other values in the dataset. Their presence can distort the arithmetic mean so that it no longer represents what is typical for the majority. This example shows that even if the majority of individuals have a low value, the mean can be heavily influenced by one or a few individuals with a very high value.

Interpretation of Statistical Averages

When using averages like the arithmetic mean, it is important to consider the distribution of the data and whether it is skewed by extreme values. Relying solely on the mean may provide an inaccurate picture of a set's central tendency, suggesting that other measures such as the median or mode might sometimes be more appropriate for describing typical values in the presence of outliers.

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