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

Answer: Its D!! I just took the test

Answer 2

The mean for the first seven weeks is given:

`(684+770+481+647+277+853+712)/(7) =632`

The median for the first seven weeks is given by the middle value of the data after being set in ascending order

277 481 647 684 712 770 853

The middle value is the 4th value, so Median = 684
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Assuming Jerry wins the price for the 8th week, the new mean is given

`(684+770+481+647+277+853+712+10000)/(8) =1803`

The new Median is now located between the 4th and 5th value, which is the mid value between 684 and 712.
A quick way to work this out is (684+712)÷2 = 698
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The increase in mean is 1803-632 = 1171
The increase in Median is 698 - 684 = 14

Correct answer is d