Question

Realtors collect data in order to serve their clients more effectively. In a recent week, data on the age of all homes sold in a particular area were collected and displayed in this histogram.

Which of the following could be the median age?

a. 19 years

b. 34 years

c. 24 years

d. 39 years

e. 29 years

Short answer

The correct option is (c)

(c) 24

Step-by-step solution

Step 1. Given information.

a. 19 years

b. 34 years

c. 24 years

d. 39 years

e. 29 years

Step 2.  The best option.

Let us first calculate the frequency associated with each bar in the histogram, which is given by the height of the bar.

Age of home (yr)	Frequency
5<10	7
10<15	8
15<20	9
20<25	7
25<30	6
30<35	3
35<40	4
40<45	2
45<50	1'
50<55	1
55<60	0
60<65	3
65<70	0
70<75	1
Total	7+8+9+7+6+3+4+2+1+1+0+3+0+1=52

The median is the middle value of the sorted data set. The data set contains 52 data values and thus the median will be between the middle between the 26th and 27th data value. Since 7+8+9 = 22 (sum frequency first three bars) and 7+8+9+7= 31 (sum frequency first four bars) and 22 < 26 <27 <31, the median has to be at the fourth bar and thus the median needs to be between 20 years and 25 years.

$20\le median<25$

As a result:

24