A city bus in Redmond, Washington contained 29 passengers. A survey revealed tha

Question

A city bus in Redmond, Washington contained 29 passengers. A survey revealed that their average yearly income was $40,000, they had a unique median income of $38,000.

(a) How large could the maximum income be?

(b) The mode of their yearly income was also $38,000, for two passengers earned exactly that, and one passenger earned just seventeen dollars more, $38,017. Then Bill Gates boarded the bus. His income that year was $30,000,000. What changes in the mean, median, and mode did his boarding cause?

Explanation / Answer

A) 14 passengers who have income below 38000 can be assumed to have 0 income and 13 of those above median can be assumed to have an income of 38001. In this scenario, the 1 person remaining will have the larrgestpossible income = 40,000x29 - 38,001x13 - 38000

= $627987

B) In this scenario, mode will remain ther same as $38,000

Median = (38000+38017)/2 = $38008.5

C) Mean = (40,000x29+30,000,000)/30 = $1,038,666.67

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