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Chapter 4: Problem 12

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 indeed be correct: 'average wage' refers to the arithmetic mean, and outliers on the higher end of the wage scale can skew this average upward meaning that more than half the population could indeed earn less than the average wage.

Step by step solution

01

Understand what 'average' means

First, understand that 'average' commonly refers to the arithmetic mean, which is calculated by summing all values and dividing by the quantity of values. In this case, the 'average wage' refers to the sum of all wages in Los Angeles divided by the number of residents who earn a wage.
02

Consider the impact of high wage earners

In any given population, some people earn significantly more than others. These high earners can pull up the arithmetic mean, or 'average wage', since their wages contribute significantly to the total sum of all wages. If, for example, a few people earn millions per year while a larger number of people earn $40,000 per year, the 'average wage' could be far above $40,000 due to the impact of those high salaries.
03

Analyze the statement

Given the potentially large disparity in wages, it's indeed possible for more than 65% of residents to earn less than the 'average wage', because outliers on the higher side can skew the average upward.

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