Find the mean of the following data. 4, 6, 7, 13, 25, and 35________

Answer

To find the mean of the given data set: 4, 6, 7, 13, 25, and 35, we will follow these steps:

### Step 1: Write down the data
The data we have is:
\[ 4, 6, 7, 13, 25, 35 \]

### Step 2: Calculate the sum of the observations
We will add all the numbers together:
\[ 4 + 6 + 7 + 13 + 25 + 35 \]
Calculating step by step:
- First, add \(4\) and \(6\):
\[ 4 + 6 = 10 \]
- Next, add \(10\) and \(7\):
\[ 10 + 7 = 17 \]
- Then, add \(17\) and \(13\):
\[ 17 + 13 = 30 \]
- Now, add \(30\) and \(25\):
\[ 30 + 25 = 55 \]
- Finally, add \(55\) and \(35\):
\[ 55 + 35 = 90 \]

So, the sum of the observations is:
\[ \text{Sum} = 90 \]

### Step 3: Count the number of observations
Next, we need to count how many numbers are in the data set:
\[ 1, 2, 3, 4, 5, 6 \]
There are \(6\) observations.

### Step 4: Apply the formula for mean
The formula for mean is:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
Substituting the values we found:
\[ \text{Mean} = \frac{90}{6} \]

### Step 5: Calculate the mean
Now, we will perform the division:
\[ \text{Mean} = 15 \]

### Final Answer
The mean of the given data is:
\[ \text{Mean} = 15 \]

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