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705-805 (Hard)|   Math Related|   Tables|      
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parkhydel
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The following table shows home sales data for 15 counties in the year 01 May 2020, 04:10
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The county with the largest median home price in 2010 had the greatest number of new constructions begin in 2010?: Yes The three counties with the lowest mean home prices in 2011 had the three lowest numbers of new constructions in 2011?: No At least half of the homes in Hutchinson county sold for less than the average home price in that county in 2011?: Yes
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The following table shows home sales data for 15 counties in the year 2011. Percent changes are taken from the prior year, 2010.

County Median
Home
Price		% Change
Median 		Mean
Home
Price $		Change
Mean		New
Constructions 		% Increase,
New
Constructions
Dempster 399,335-0.5392,414-0.914,445-0.4
Hill 424,259-2.4473,802-0.522,0501.2
Hoff 376,825-1.4384,289-1.119,025-0.9
Hutchinson 409,742-2.5426,314-0.217,2550.3
Lanzillotti 359,204-0.8363,828-1.416,220-1.8
Malave 384,874-1.4389,516-1.215,535-0.3
Meyer 374,214-1.8373,219-1.419,265-0.4
Miller 362,877-1.9371,820-1.719,235-2.1
Patrick 382,414-1.4380,224-1.313,460-0.3
Peck 414,380-1.9412,442-0.821,1251.5
Pierce 402,654-1.8406,809-1.220,6800.6
Portnoy 348,802-2.1351,225-2.418,420-1.8
Rechner 355,283-1.7353,235-1.618,920-1.1
Slade 404,289-2.7401,357-2.918,8400.2
White 344,218-2.6348,941-2.816,645-1.4

Which of the following conclusions can be drawn from the table above?

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Yes No
The county with the largest median home price in 2010 had the greatest number of new constructions begin in 2010?
The three counties with the lowest mean home prices in 2011 had the three lowest numbers of new constructions in 2011?
At least half of the homes in Hutchinson county sold for less than the average home price in that county in 2011?
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The county with the largest median home price in 2010 had the greatest number of new constructions begin in 2010?: Yes The three counties with the lowest mean home prices in 2011 had the three lowest numbers of new constructions in 2011?: No At least half of the homes in Hutchinson county sold for less than the average home price in that county in 2011?: Yes
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napolean92728
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The following table shows home sales data for 15 counties in the year 08 Apr 2025, 02:57
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So boil down to the surface, median is the middle value of any given dataset and if it's less than mean it clearly means that at least half of the values are below mean and so the answer is clear.
7Amulya
Hi,

Can you elaborate on 3 question. How did we figure out from number of new construction that almost half sold for less than mean price?

bM22
1. The county with the largest median home price in 2010 had the greatest number of new constructions begin in 2010?

The county with the largest median home price in 2010 - Hill, since it has the highest in 2011, even after a decrease of 2.4%,
now the country with the highest number of new constructions begin in 2010 = can be either Hill or Peck, so

for Hill let the number of new constructions in 2010 was x, therefore,
x+(1.2/100)x = 22050, which on solving we get x as: 21788

or Peck let the number of new constructions in 2010 was y, therefore,
y+(1.5/100)y = 21125, which on solving we get x as: 20812,

we can see that Hill has the highest number of new constructions begin in 2010,

So Yes, 1 can be concluded from the data mentioned in the table.


2. The three counties with the lowest mean home prices in 2011 had the three lowest numbers of new constructions in 2011?
Now the 3 countries with the lowest mean home prices in 2011 are: White, Portnoy and Rechner, in this order.
Now we need to check if they had the three lowest numbers of new constructions in 2011 - Patrick, Dempster and Malave.

So No, the 3 countries with the lowest mean home prices in 2011 did not have the 3 lowest numbers of new construction in 2011.


3. At least half of the homes in Hutchinson county sold for less than the average home price in that county in 2011?
So for Hutchinson - mean home price is : 426314, and median home price is: 409742 and we also know the number of new constructions in 2011 - 17255.
Now mean is close but, not lower than the median and if we look at the total no. of new constructions => almost half sold for < mean price.

So Yes.
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Apt0810
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The following table shows home sales data for 15 counties in the year 01 May 2020, 05:41
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1)Yes, since Hill which has high Median home price, had the greatest construction in 2010 since in 2011 it has a 1.2% increment so in 2010 it was 22050/1.012= 21788

3)No, since Patrtick is not included in the list

4)Yes, since avg is 426314 and median is 409742 and total number of construction is 17255 so at least half of the homes were sold for less than avg price
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The following table shows home sales data for 15 counties in the year 01 May 2020, 12:43
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1. The county with the largest median home price in 2010 had the greatest number of new constructions begin in 2010?

The county with the largest median home price in 2010 - Hill, since it has the highest in 2011, even after a decrease of 2.4%,
now the country with the highest number of new constructions begin in 2010 = can be either Hill or Peck, so

for Hill let the number of new constructions in 2010 was x, therefore,
x+(1.2/100)x = 22050, which on solving we get x as: 21788

or Peck let the number of new constructions in 2010 was y, therefore,
y+(1.5/100)y = 21125, which on solving we get x as: 20812,

we can see that Hill has the highest number of new constructions begin in 2010,

So Yes, 1 can be concluded from the data mentioned in the table.


2. The three counties with the lowest mean home prices in 2011 had the three lowest numbers of new constructions in 2011?
Now the 3 countries with the lowest mean home prices in 2011 are: White, Portnoy and Rechner, in this order.
Now we need to check if they had the three lowest numbers of new constructions in 2011 - Patrick, Dempster and Malave.

So No, the 3 countries with the lowest mean home prices in 2011 did not have the 3 lowest numbers of new construction in 2011.


3. At least half of the homes in Hutchinson county sold for less than the average home price in that county in 2011?
So for Hutchinson - mean home price is : 426314, and median home price is: 409742 and we also know the number of new constructions in 2011 - 17255.
Now mean is close but, not lower than the median and if we look at the total no. of new constructions => almost half sold for < mean price.

So Yes.
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The following table shows home sales data for 15 counties in the year 28 Nov 2024, 09:12
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Hi,

Can you elaborate on 3 question. How did we figure out from number of new construction that almost half sold for less than mean price?

bM22
1. The county with the largest median home price in 2010 had the greatest number of new constructions begin in 2010?

The county with the largest median home price in 2010 - Hill, since it has the highest in 2011, even after a decrease of 2.4%,
now the country with the highest number of new constructions begin in 2010 = can be either Hill or Peck, so

for Hill let the number of new constructions in 2010 was x, therefore,
x+(1.2/100)x = 22050, which on solving we get x as: 21788

or Peck let the number of new constructions in 2010 was y, therefore,
y+(1.5/100)y = 21125, which on solving we get x as: 20812,

we can see that Hill has the highest number of new constructions begin in 2010,

So Yes, 1 can be concluded from the data mentioned in the table.

2. The three counties with the lowest mean home prices in 2011 had the three lowest numbers of new constructions in 2011?
Now the 3 countries with the lowest mean home prices in 2011 are: White, Portnoy and Rechner, in this order.
Now we need to check if they had the three lowest numbers of new constructions in 2011 - Patrick, Dempster and Malave.

So No, the 3 countries with the lowest mean home prices in 2011 did not have the 3 lowest numbers of new construction in 2011.


3. At least half of the homes in Hutchinson county sold for less than the average home price in that county in 2011?
So for Hutchinson - mean home price is : 426314, and median home price is: 409742 and we also know the number of new constructions in 2011 - 17255.
Now mean is close but, not lower than the median and if we look at the total no. of new constructions => almost half sold for < mean price.

So Yes.
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The following table shows home sales data for 15 counties in the year 06 Sep 2025, 04:54
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here, what is the relevance of total no. of new construction 17255, while median home price and mean home price giving answer?please explain
napolean92728
So boil down to the surface, median is the middle value of any given dataset and if it's less than mean it clearly means that at least half of the values are below mean and so the answer is clear.

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The following table shows home sales data for 15 counties in the year 22 Oct 2025, 18:53
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I feel the question is a bit ambiguous. When they say "new constructions", are they referring to constructions completed in the given year or constructions that started that year? You are assuming they started that year (or started and finished the same year). I marked No cause we can't make the inference of when they began construction
bM22
1. The county with the largest median home price in 2010 had the greatest number of new constructions begin in 2010?

The county with the largest median home price in 2010 - Hill, since it has the highest in 2011, even after a decrease of 2.4%,
now the country with the highest number of new constructions begin in 2010 = can be either Hill or Peck, so

for Hill let the number of new constructions in 2010 was x, therefore,
x+(1.2/100)x = 22050, which on solving we get x as: 21788

or Peck let the number of new constructions in 2010 was y, therefore,
y+(1.5/100)y = 21125, which on solving we get x as: 20812,

we can see that Hill has the highest number of new constructions begin in 2010,

So Yes, 1 can be concluded from the data mentioned in the table.


2. The three counties with the lowest mean home prices in 2011 had the three lowest numbers of new constructions in 2011?
Now the 3 countries with the lowest mean home prices in 2011 are: White, Portnoy and Rechner, in this order.
Now we need to check if they had the three lowest numbers of new constructions in 2011 - Patrick, Dempster and Malave.

So No, the 3 countries with the lowest mean home prices in 2011 did not have the 3 lowest numbers of new construction in 2011.


3. At least half of the homes in Hutchinson county sold for less than the average home price in that county in 2011?
So for Hutchinson - mean home price is : 426314, and median home price is: 409742 and we also know the number of new constructions in 2011 - 17255.
Now mean is close but, not lower than the median and if we look at the total no. of new constructions => almost half sold for < mean price.

So Yes.
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The following table shows home sales data for 15 counties in the year 29 Dec 2025, 02:08
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(1) The county with the largest median home price in 2010 had the greatest number of new constructions begin in 2010?
- pay attention it is 2010, not the same table presented in 2011. do we have the data of 2010? yes, we have the % increase from the previous year which in 2010. so check from that % filter.
- start by getting the % new construction increase and we get PECK at 1.5
- check is PECK % change median and median home price. We get it is the 2nd largest median with -1.9% increased
- We can guesstimate PECK in 2010 is larger in median home price than HILL or HUTCHISON (from the 1st or 3rd largest in 2011)
- Hence, YES

(2) The three counties with the lowest mean home prices in 2011 had the three lowest numbers of new constructions in 2011?
- filter it to the LOWEST new constructiosn and we get PETRICK, DEMPSTER, MALAVE
- check it with the LOWEST mean home price and we get WHITE, PORTNOY, RECHER
- It has different counties,
- Hence, NO

(3) At least half of the homes in Hutchinson county sold for less than the average home price in that county in 2011?
- Focus the data in HUTCHISON county
- Identify the question: AT LEAST HALF meaning >=50% or more than half
- the average home price in 2011 in Huchison: 426,314
- The Qs asked is >=50% price home < 426,314???
- We can check from the MEDIAN price home is 409,742, meaning more than 50% home price is less than 425.314
- Hence, YES
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