The mean purchase total is $93.80 and the median purchase total is $75.80. The store manager investigates and learns that the customer that made a $500 purchase had not purchased groceries, but rather a $500 gift card. Because this customer’s purchase was not typical, the manager decides to exclude this total from the data set. How will removing the $500 purchase from the data set affect the value of the mean and the median?

(A) The mean will decrease more than the median.
(B) The mean will decrease less than the median.
(C) The mean will stay the same, but the median will decrease.
(D) The mean will increase more than the median.
(E) The mean will increase, but not as much as the median.

(A) The mean will decrease more than the median.

Step-by-step explanation:

$500 is much more than the mean of $93.80, so removing it from the data set will decrease the mean significantly.  The median of $75.80 will move to the next smaller number, so the change will be small or even none.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4