Question

Use the table to answer the 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?


(1 point)

Answer 1

To find the median value of the houses based on the provided data, we need to list out the values of all the houses according to the number of houses associated with each property value.

From the table, we can list the values as follows:

- $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 let's write down all the house values:

- $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 count the total number of houses:

- 2 (from $150,000)
- 4 (from $220,000)
- 3 (from $490,000)
- 2 (from $540,000)
- 5 (from $800,000)
- 2 (from $975,000)

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

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

Now, let's list the values in order:
1. $150,000 (1)
2. $150,000 (2)
3. $220,000 (3)
4. $220,000 (4)
5. $220,000 (5)
6. $220,000 (6)
7. $490,000 (7)
8. $490,000 (8)
9. $490,000 (9)
10. $540,000 (10)
11. $540,000 (11)
12. $800,000 (12)
13. $800,000 (13)
14. $800,000 (14)
15. $800,000 (15)
16. $800,000 (16)
17. $975,000 (17)
18. $975,000 (18)

The 9th value is **$490,000**, and the 10th value is **$540,000**.

Now, we find the median:

\[
\text{Median} = \frac{\text{9th value} + \text{10th value}}{2} = \frac{490,000 + 540,000}{2} = \frac{1,030,000}{2} = 515,000
\]

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