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Chapter 4: Problem 10

Consider the following statement: More than \(65 \%\) of the residents of Los Angeles earn less than the average wage for that city. Could this statement be correct? If so, how? If not, why not?

Short Answer

Expert verified
Yes, the statement could be correct. It's possible for more than \(65 \%\) of residents to earn less than the 'average' wage in Los Angeles, especially if a small percentage of residents have highly inflated wages. This happens due to the nature of 'mean' which could be pulled upwards by extremely high values, separating it from the median which represents the middle wage of the whole population.

Step by step solution

01

Understand the problem

Firstly, understand the statement: 'More than \(65 \%\) of the residents of Los Angeles earn less than the 'average' wage for that city.' The 'average' wage here means the 'mean' wage, which is calculated by summing all the wages and dividing by the total number of people.
02

Analyze Average Vs. Median

The 'average' or 'mean' wage could be heavily influenced by high salaries. For instance, if a small percentage of people earn an exceedingly high wage, the 'average' will be skewed towards these high numbers. The median wage, on the other hand, is the middle value in the data set when all wages are ordered from smallest to largest. Therefore, it's plausible for the majority of people (more than \(50\%\)) to earn less than the 'average' wage, because this average can be skewed by high earners.
03

Apply to the current scenario

For Los Angeles, it's plausible that more than \(65 \%\) of residents earn less than the 'average' wage, if a small percentage of residents have exceedingly high wages. Remember that the 'average' is being pulled up by these high wages, hence it could be higher than the income of the majority of the residents.

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Most popular questions from this chapter

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