Chapter B.2, Problem 14E

(a)

To determine

To find: The mean, mode and median of the prices.

Answer to Problem 14E

Mean of the price is $\$2,755,000$ .

Median of the price is $\$462,500$ .

Modes of the price are $\$425,000$ , $\$500,000$ and $\$550,000$ .

Explanation of Solution

Given information: The selling price of 12 new homes in one subdivision are given.

Formula used:

1. The mean, or average, of n numbers is the sum of the numbers divided by n.
2. The median of n numbers is the middle number when the numbers are written in ascending order. If n is even, then the median is the average of the two middle numbers.
3. The mode of n numbers is the number that occurs most frequently.

Calculation:

The mean of the prices is

Mean $=\frac{525,000+375,000+425,000+\mathrm{...}+450,000}{12}$

  $\begin{array}{l}=\frac{5,510,000}{2}\\ =\$2,755,000\end{array}$

To find the median, order the prices as follows.

  $\$350,000$$\$375,000$$\$385,000$$\$425,000$

  $\$425,000$$\$450,000$$\$475,000$$\$500,000$

  $\$500,000$$\$525,000$$\$550,000$$\$550,000$

From this list, we can see that the median price is $\frac{450,000+475,000}{2}=\frac{925,000}{2}=\$462,500$

Since, $\$425,000$ , $\$500,000$ and $\$550,000$ occur two times.

So, the modes are $\$425,000$ , $\$500,000$ and $\$550,000$ .

Thus, mean of the price is $\$2,755,000$ .

Median of the price is $\$462,500$ .

Modes of the price are $\$425,000$ , $\$500,000$ and $\$550,000$ .

(b)

To determine

To find: The measure of central tendency which best describe the prices.

Answer to Problem 14E

Median best describes the prices.

Explanation of Solution

Given information: The selling price of 12 new homes in one subdivision are given.

Formula used:

1. The mean, or average, of n numbers is the sum of the numbers divided by n.
2. The median of n numbers is the middle number when the numbers are written in ascending order. If n is even, then the median is the average of the two middle numbers.
3. The mode of n numbers is the number that occurs most frequently.

Since, mean of the price is $\$2,755,000$ .

Median of the price is $\$462,500$ .

Modes of the price are $\$425,000$ , $\$500,000$ and $\$550,000$ .

So, the median is the most representative measure.

Thus, median best describes the prices.