The distribution of individual incomes in the United States is strongly skewed to the right. In 2013, the mean and median incomes of the top 5% of Americans were $196,723 and $322,343. Which of these numbers is the mean and which is the median? Explain your reasoning and roughly sketch the shape of the distribution identifying where the mean and median fall

Question

Mathematics

Guillermo Gregory

11 February, 10:34

The distribution of individual incomes in the United States is strongly skewed to the right. In 2013, the mean and median incomes of the top 5% of Americans were $196,723 and $322,343. Which of these numbers is the mean and which is the median? Explain your reasoning and roughly sketch the shape of the distribution identifying where the mean and median fall

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Answers (1)

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Heidy Banks · Answer 1

The mean would be $322,343 and the median would be $196,723.

Step-by-step explanation:

Since the distribution of individual incomes is skewed to the right, it means that the distribution has a long right tail.

Drawing a distribution with this characteristic, we can see how the majority of the data falls into the left side of the graphic, meaning that a lot of people receive less income. Following this reasoning, the mean which is the amount of the data (in this case individual income) divided by the amount of people, would be the higher number, meaning that the few people who earn more money would influence in making this number higher.

Following this reasoning, the median (which is not influenced by this difference) would be the less high number.