Question

Jerry has been a returning contestant on a game show for the last seven weeks. In a contestant's first seven appearances on the show they have a chance to answer one question and win anywhere between $200-$900. On their eighth appearance they get a chance to answer a question worth $10,000. Given Jerry's winnings in the following table, describe what would happen to the mean and median of the data set if he were to get the Week 8 question right.

Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
$684
$770
$481
$647
$277
$853
$712
a.
The mean increases by $1,803, the median increases by $698.
b.
The mean decreases by $1,803, the median decreases by $698.
c.
The mean decreases by $1,171, the median decreases by $14.
d.
The mean increases by $1,171, the median increases by $14.

Answer 1

Calculate the current mean and median, then add the $10,000 and recalc.

Sum of weeks 1–7 = 684+770+481+647+277+853+712 = 4,424.
Current mean = 4,424/7 = 632.
Sorted data: 277, 481, 647, 684, 712, 770, 853 → median = 684.

Add $10,000: new sum = 14,424, new mean = 14,424/8 = 1,803 (increase = 1,803 − 632 = 1,171).
New sorted list: 277, 481, 647, 684, 712, 770, 853, 10,000 → median = (684+712)/2 = 698 (increase = 14).

So the mean increases by 1,171 and the median increases by 14 — answer d.