Discuss the below:
The Median and Mean Prize Amount on TV Show, Deal or No Deal
Q: 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) Using only the table, determine the median prize amount.
(b) Without doing any calculations, how do you expect the mean to compare to the median prize amount? Explain.
(c) Use technology to compute the mean of the prize amounts.
(d) Did your calculation confirm your prediction from part (b)? Are the mean and median close to each other? Explain why this makes sense.
(e) How many and what proportion of the prize amounts are greater than the mean?
(f) How many and what proportion of the prize amounts are greater than the median?
(g) 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.