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# The Median and Mean Prize Amount on TV Show, Deal or No Deal

On the TV show Deal or No Deal, a contestant chooses from among 26 suitcases, each containing a dollar amount. These dollar amounts are typically:

.01 1 5 10 25 50 75 100 200
300 400 500 750 1,000 5,000 10,000 25,000 50,000
75,000 100,000 200,000 300,000 400,000 500,000 750,000 1,000,000

(a) (2) Using only the table, determine the median prize amount.

(b) (4) Without doing any calculations, how do you expect the mean to compare to the median prize amount? Explain.

(c) (3) Use technology to compute the mean of the prize amounts.

(d) (3) Did your calculation confirm your prediction from part (b)? Are the mean and median close to each other? Explain why this makes sense.

(e) (3) How many and what proportion of the prize amounts are greater than the mean?

(f) (2) How many and what proportion of the prize amounts are greater than the median?

(g) (3) If the producers of the show want to advertise either the mean or median prize amount in order to give the impression that contestants win huge amounts of money, which (mean or median) should they advertise. Explain.

#### Solution Preview

(a) The median is (750 + 1000)/2 = 875 dollars

(b) We would expect the mean to be much larger than the median prize amount since the mean is a lot more sensitive
to the very large outliers of the data set while the median is just the middle of the data set and is not affected by outliers.

(c) The ...

#### Solution Summary

The solution computes the median and mean prize amount on television show, Deal or No Deal.

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