which average

[red and white kop!]

a newspaper makes the folloxing statement: over 60% of houses sold this month were sold for more than the average selling price
consider the possible truth of this statement and what is meant by average (median, mean, mode)

i know this must be easy but its the notion i have a hard times getting around. i understand that it can be the mode and it can't be the median but i don't understand how to fit in a the mean.

 

[Deleted member 4993]

a newspaper makes the folloxing statement: over 60% of houses sold this month were sold for more than the average selling price
consider the possible truth of this statement and what is meant by average (median, mean, mode)

i know this must be easy but its the notion i have a hard times getting around. i understand that it can be the mode and it can't be the median but i don't understand how to fit in a the mean.

Suppose there were 100 houses - with average price A.

Then 60 houses sold at above A. Assume average of those 60 houses is A[sub:3hf2u579]p[/sub:3hf2u579]. Also Assume A[sub:3hf2u579]p[/sub:3hf2u579] = A + x[sub:3hf2u579]p[/sub:3hf2u579]

Then 40 houses sold at belowA. Assume average of those 40 houses is A[sub:3hf2u579]m[/sub:3hf2u579]. Also Assume A[sub:3hf2u579]m[/sub:3hf2u579] = A - x[sub:3hf2u579]m[/sub:3hf2u579]

Thus

100 * A = 60* (A + x[sub:3hf2u579]p[/sub:3hf2u579]) + 40*(A - x[sub:3hf2u579]m[/sub:3hf2u579])

x[sub:3hf2u579]m[/sub:3hf2u579] = 1.5* x[sub:3hf2u579]p[/sub:3hf2u579])

So if A = 100,000 then x[sub:3hf2u579]p[/sub:3hf2u579] = 10,000 and x[sub:3hf2u579]m[/sub:3hf2u579] = 15000 - will satisfy the condition.

In other words if you sell 60 houses for 110,000 and 40 houses for 85,000 - you will satisfy the condition.