What is the average of the set `{-1, 3, 7, 11, 15, 19, 23,27}` ?

Answer

To find the average of the set \(\{-1, 3, 7, 11, 15, 19, 23, 27\}\), we will follow these steps:

### Step 1: Identify the numbers in the set
The numbers in the set are:
\[ -1, 3, 7, 11, 15, 19, 23, 27 \]

### Step 2: Calculate the total sum of the numbers
We will sum all the numbers in the set:
\[ \text{Total Sum} = -1 + 3 + 7 + 11 + 15 + 19 + 23 + 27 \]

Calculating this step-by-step:
- First, add \(-1\) and \(3\):
\[ -1 + 3 = 2 \]
- Next, add \(2\) and \(7\):
\[ 2 + 7 = 9 \]
- Then, add \(9\) and \(11\):
\[ 9 + 11 = 20 \]
- Now, add \(20\) and \(15\):
\[ 20 + 15 = 35 \]
- Next, add \(35\) and \(19\):
\[ 35 + 19 = 54 \]
- Then, add \(54\) and \(23\):
\[ 54 + 23 = 77 \]
- Finally, add \(77\) and \(27\):
\[ 77 + 27 = 104 \]

So, the total sum of the numbers is:
\[ \text{Total Sum} = 104 \]

### Step 3: Count the number of items in the set
Next, we count how many numbers are in the set. The set has:
\[ 1, 2, 3, 4, 5, 6, 7, 8 \quad (\text{8 items}) \]

### Step 4: Calculate the average
Now, we can calculate the average using the formula:
\[ \text{Average} = \frac{\text{Total Sum}}{\text{Number of Items}} = \frac{104}{8} \]

Calculating this gives:
\[ \text{Average} = 13 \]

### Final Answer
The average of the set \(\{-1, 3, 7, 11, 15, 19, 23, 27\}\) is:
\[ \boxed{13} \]