Certainly! Let's calculate the mean of the given data set step by step. The data set provided is:
[tex]\[ 53, 35, 82, 94, 93, 63, 44, 74 \][/tex]
### Step 1: Sum Up All the Data Points
First, we need to calculate the sum of all the incomes. Let's add them together:
[tex]\[ 53 + 35 + 82 + 94 + 93 + 63 + 44 + 74 \][/tex]
### Step 2: Count the Number of Data Points
Next, count how many data points there are in the data set.
There are 8 incomes in the list.
### Step 3: Calculate the Mean
To find the mean (average), we divide the sum of the data points by the number of data points.
[tex]\[ \text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}} \][/tex]
### Step 4: Calculate and Round the Mean
Perform the division and round the result to one decimal place:
[tex]\[ \text{Mean} = \frac{538}{8} = 67.25 \][/tex]
Rounded to one decimal place, the mean is [tex]\( 67.2 \)[/tex].
So, the mean annual income for the given data set is:
[tex]\[ \boxed{67.2 \text{ thousands of dollars}} \][/tex]
