What other examples can you think of where most people have more or less than the...

What other examples can you think of where most people have more or less than the average? This is true of most things with a non-symmetric distribution (e.g., weight, math scores, marathon times) but it is nice to continue the theme of the video in terms of risk (e.g., most have below average risk of a automobile accident, death by violence, or even, say, getting a date).

Solutions

Expert Solution

here median < mean

this is positive skewed

Example

Distribution of Income

If the distribution of the household incomes of a region is studied, from values ranging between $5,000 to $250,000, most of the citizens fall in the group between $5,000 and $100,000, which forms the bulk of the distribution towards the left side of the distribution, which is the lower side. However, a couple of individuals may have a very high income, in millions. This makes the tail of extreme values (high income) extend longer towards the positive, or right side. Thus, it is a positively skewed distribution.

Marks obtained on difficult test

If a test conducted in a school has a high difficulty level, then most of the students will have a poor-to-average performance in it. This bulk of students will form the maximum part of the distribution, towards the left side of the positively skewed distribution curve. The highest marks in the test will be obtained only by a couple of meritorious students, which forms the right tail of extreme values. The students with very high marks will shift the mean towards the right, making it a positively skewed distribution. In other words, there will be a higher frequency of low scores and a lower frequency of high scores.

Neighborhood Housing Prices

The variation in housing prices is a positively skewed distribution. For example, if a neighborhood has 100 houses, with 99 of them having a price of $100,000, while only one sells at $1,000,000, then the frequency of houses selling at $100,000 will be maximum towards the left side of the distribution, since it is a lower value than $1,000,000. However, the single house priced at $1,000,000 will push the mean higher, and result in a long tail towards the right side, making it a positively skewed distribution.

milcah answered 9 months ago

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