To determine the mean number of gallons of milk consumed by these families last month, we will follow these steps:
1. Calculate the total number of families included in the survey.
2. Calculate the total amount of milk consumed by all families.
3. Determine the mean number of gallons of milk consumed per family.
### Step 1: Total Number of Families
We first sum the number of families in all categories:
[tex]\[
3 + 10 + 10 + 15 = 38
\][/tex]
Thus, the total number of families is 38.
### Step 2: Total Amount of Milk Consumed
Next, we calculate the total gallons of milk consumed by multiplying the number of families by the gallons of milk consumed and then summing these products:
[tex]\[
(3 \times 3) + (10 \times 4) + (10 \times 5) + (15 \times 6) = 9 + 40 + 50 + 90 = 189
\][/tex]
So, the total number of gallons of milk consumed by all 38 families is 189.
### Step 3: Mean Number of Gallons of Milk Consumed
To find the mean number of gallons of milk consumed, we divide the total gallons of milk consumed by the total number of families:
[tex]\[
\text{Mean} = \frac{\text{Total Gallons of Milk}}{\text{Total Number of Families}} = \frac{189}{38} \approx 4.973684210526316
\][/tex]
Rounding this to at least one decimal place, we get:
[tex]\[
\text{Mean} \approx 5.0
\][/tex]
Thus, the mean number of gallons of milk consumed last month by these families is approximately [tex]\( \boxed{5.0} \)[/tex] gallons.
