Question

Find the mode, median and mean for each data set.
Single Family Home Prices
276,900
270,400
283,600
281,800
279,400
285,600
283,100
301,400
278,400
278,800

Answer 1

Let's calculate the mode, median, and mean for the given data set of single-family home prices.

### Data Set:
276,900
270,400
283,600
281,800
279,400
285,600
283,100
301,400
278,400
278,800

### Step 1: Mode
The **mode** is the value that appears most frequently in a data set. In this case, each number appears only once, so there is **no mode** for this data set.

### Step 2: Median
To find the **median**, we first need to arrange the data in ascending order:

1. 270,400
2. 276,900
3. 278,400
4. 278,800
5. 279,400
6. 281,800
7. 283,100
8. 283,600
9. 285,600
10. 301,400

Since there are 10 numbers (an even count), the median will be the average of the 5th and 6th values:

- 5th value: 279,400
- 6th value: 281,800

\[
\text{Median} = \frac{(279,400 + 281,800)}{2} = \frac{561,200}{2} = 280,600
\]

### Step 3: Mean
The **mean** is calculated by summing all the values and dividing by the count of numbers.

\[
\text{Sum} = 270,400 + 276,900 + 278,400 + 278,800 + 279,400 + 281,800 + 283,100 + 283,600 + 285,600 + 301,400
\]
\[
\text{Sum} = 2,797,300
\]

Now, divide by the number of items in the data set (10):

\[
\text{Mean} = \frac{2,797,300}{10} = 279,730
\]

### Summary:
- **Mode**: None
- **Median**: 280,600
- **Mean**: 279,730