Question

The May 1, 2009, issue of a certain publication reported the following home sale amounts for a sample of homes in Alameda, CA that were sold the previous month (1,000s of $).

595 812 575 606 345 1,280 408 537 559 674

(a) Calculate and interpret the sample mean and median. The sample mean is x =_________ thousand dollars and the sample median is =_________ thousand dollars. This means that the average sale price for a home in this sample was $ and that half the sales were for less than the__________ price, while half were more than the________ price.

(b) Suppose the 6th observation had been 985 rather than 1,280. How would the mean and median change?

Changing that one value raises the sample mean but has no effect on the sample median.

Changing that one value has no effect on the sample mean but raises the sample median.

Changing that one value has no effect on either the sample mean nor the sample median.

Changing that one value lowers the sample mean but has no effect on the sample median.

Changing that one value has no effect on the sample mean but lowers the sample median.

(c) Calculate a 20% trimmed mean by first trimming the two smallest and two largest observations. (Round your answer to the nearest hundred dollars.)

$ ?

(d) Calculate a 15% trimmed mean. (Round your answer to the nearest hundred dollars.)

$?

Answer 1

	Sale price(X)
	595
	812
	575
	606
	345
	1280
	408
	537
	559
	674
Total	6391

Here,

Sum of the observations = 6391

Number of observations (n) =10

For finding median , arrange the data in ascending order as

Obsn #	Sale price(X)
1	345
2	408
3	537
4	559
5	575
6	595
7	606
8	674
9	812
10	1280

  

  

  

  

a)

The sample mean is x =_____639.1____ thousand dollars and the sample median is =__585_______ thousand dollars. This means that the average sale price for a home in this sample was $639.1 thousand and that half the sales were for less than the $585 thousand_ price, while half were more than the_$585 thousand________ price.

b)

Suppose the 6th observation had been 985 rather than 1,280.

Changing that one value lowers the sample mean but has no effect on the sample median.

c)

After trimming  first two smallest and two largest observations we get

	Sale price(X)
	537
	559
	575
	595
	606
	674
Total	3546

Here

n = 6

Sum of the observations = 3546

Now

20% trimmed mean is given by

A 20% trimmed mean by first trimming the two smallest and two largest observations is $591 thousand.

d)

If you need to calculate the 15% trimmed mean of a sample containing 10 entries, strictly this would mean discarding 1 point from each end (equivalent to the 10% trimmed mean).

So,

The data after trimming smallest and largest value , we get

	Sale price(X)
	408
	537
	559
	575
	595
	606
	674
	812
Total	4766

Here

n = 8

Sum of the observations = 4766

Now

15% trimmed mean is given by

  

~ 596

Therefore, a 15% trimmed mean = $596 thousand