Use the table to answer the question.

Question

This table presents the number of houses corresponding to different property values, showing the distribution of home prices in a given dataset.
Value per House Number of Houses
$150,000
2
$220,000
4
$490,000
3
$540,000
2
$800,000
5
$975,000
2
The values of several houses on Mango Street are displayed on the table. What is the median value of these houses?

Answer 1

To find the median value of the houses, we first need to list all the values according to their frequency. Here is the breakdown of the house values based on the table you provided:

• $150,000: 2 houses
• $220,000: 4 houses
• $490,000: 3 houses
• $540,000: 2 houses
• $800,000: 5 houses
• $975,000: 2 houses

Now, list the values considering their frequency:

• $150,000, $150,000
• $220,000, $220,000, $220,000, $220,000
• $490,000, $490,000, $490,000
• $540,000, $540,000
• $800,000, $800,000, $800,000, $800,000, $800,000
• $975,000, $975,000

Now we can count the total number of houses:

• Total: 2 + 4 + 3 + 2 + 5 + 2 = 18 houses

To find the median, we need to find the middle value in this ordered list. Since there are 18 houses (an even number), the median will be the average of the 9th and 10th values.

Counting the values ordered in list:

1. $150,000
2. $150,000
3. $220,000
4. $220,000
5. $220,000
6. $220,000
7. $490,000
8. $490,000
9. $490,000 (9th value)
10. $540,000 (10th value)
11. $540,000
12. $800,000
13. $800,000
14. $800,000
15. $800,000
16. $800,000
17. $975,000
18. $975,000

Now, taking the values at positions 9 and 10:

• 9th value: $490,000
• 10th value: $540,000

To find the median, calculate the average of these two values:

\[ \text{Median} = \frac{490,000 + 540,000}{2} = \frac{1,030,000}{2} = 515,000 \]

Thus, the median value of the houses is $515,000.