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Do we agree on this point now?

No. The article's numbers are based on median value not average value, so your example isn't relevant. To get the published median value to work in your example, townhome prices would indeed have to fall a bit. The shocking statistic that I'd observe in your example is that sales of houses greater than a million dollars fell by 50% in one month.

You are correct:

"Median" is not the same as "Mean" nor the same as "Mode".

From my (admittedly simple) example, the "median" price of all houses sold in August was $100,000 and the "median" price of all houses sold in September was $105,000.

And the "mode" for all houses sold in August was $100,000 while the "mode" for all houses sold in September was $105,000.

Given the assumptions I presented, neither of these last two statistics is very useful, IMHO.

Nevertheless...

Let's look at two months of assumed sales data in which each house (in an admittedly small sample) has a different selling price to see what can happen to the "Median", in spite of price inflation, if fewer "expensive homes" are sold in "Month 2" than "Month 1".

11 Sales in.........9 Sales in
Month One.........Month Two
Model..$Price.....Model..$Price

A.....100,000.....A.....105,000
B.....110,000.....B.....115,500
C.....120,000.....C.....126,000
D.....130,000.....D.....136,500
E.....140,000.....E.....147,000
F.....150,000.....F.....157,500
G.....160,000.....G.....168,000
H.....170,000.....H.....178,500
I......180,000.....I.....189,000
J......190,000
K.....200,000

Median: $150,000 $147,000

Do you agree?

BTW, I agree with you that if the number of less expensive homes sold should increase in Month 2, those sales would also cause the "Median" to decrease. As a quick example, if three Model "A" homes were sold in Month 2 instead of just one, thereby keeping the total number of homes sold at 11, the "Median" price would drop to $136,500.

So I think my point is still valid: The application of statistical analysis to diverse data populations can create useless (but "dramatic" and "newsworthy") conclusions.

You are correct:

"Median" is not the same as "Mean" nor the same as "Mode".

From my (admittedly simple) example, the "median" price of all houses sold in August was $100,000 and the "median" price of all houses sold in September was $105,000.

And the "mode" for all houses sold in August was $100,000 while the "mode" for all houses sold in September was $105,000.

Given the assumptions I presented, neither of these last two statistics is very useful, IMHO.

Nevertheless...

Let's look at two months of assumed sales data in which each house (in an admittedly small sample) has a different selling price to see what can happen to the "Median", in spite of price inflation, if fewer "expensive homes" are sold in "Month 2" than "Month 1".

11 Sales in.........9 Sales in
Month One.........Month Two
Model..$Price.....Model..$Price

A.....100,000.....A.....105,000
B.....110,000.....B.....115,500
C.....120,000.....C.....126,000
D.....130,000.....D.....136,500
E.....140,000.....E.....147,000
F.....150,000.....F.....157,500
G.....160,000.....G.....168,000
H.....170,000.....H.....178,500
I......180,000.....I.....189,000
J......190,000
K.....200,000

Median: $150,000 $147,000

Do you agree?

BTW, I agree with you that if the number of less expensive homes sold should increase in Month 2, those sales would also cause the "Median" to decrease. As a quick example, if three Model "A" homes were sold in Month 2 instead of just one, thereby keeping the total number of homes sold at 11, the "Median" price would drop to $136,500.

So I think my point is still valid: The application of statistical analysis to diverse data populations can create useless (but "dramatic" and "newsworthy") conclusions.