ExplanationQuestion 20The number of homes sold is given in the table, and the mean of the prices is given in the line graph.
The mean price of the 700 homes sold in 2012 and 2013 is the weighted average of the mean price of the 410 homes sold in 2012, which is $250,000, and the mean price of the 290 homes sold in 2013, which is $300,000:
\(\frac{(410*($250,000)+290*($300,000))}{700} = $270,714\).
Of the choices given, the closest is $270,000. The correct answer is
Choice B.
Question 21The median prices are given in the line graph. The median price decreased from $200,000 in 2011 to $150,000 in 2012, which is a decrease of $50,000. As a percent of the 2011 price, this is \(\frac{(50,000)}{(200,000)}*100%\), or 25%. The correct answer is
Choice C.
Question 22For each year, the sum of the prices is equal to the number of homes sold times the mean price of the homes sold.
For 2010, the sum is equal to (351)($275,000), or $96,525,000.
For 2009, the sum is (503)($250,000), or $125,750,000, which is greater than the sum for 2010. So statement A is false.
For 2011, the sum is (390)($175,000), or $68,250,000, which is less than the sum for 2010. So statement B is true.
Since the sum for 2009 is greater than the sum for 2011, statement C is true.
The correct answer consists of
Choices B and C.
Question 23The total price of all the homes sold in 2009 is equal to the number of homes sold times the mean price of the homes sold. The tax is 3% of this amount. Since the choices given are far apart, there is no need for accurate computations. Using estimation, you get a total price of about (500) ($250,000), or $125 million. The tax of 3% is (0.03)($125 million), or approximately $3.75 million. Of the choices given, $3,800,000 is closest to this amount. The correct answer is
Choice E.
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