Sure! Let's find the median number of children among the 110 families as per the given table step-by-step.
### Step 1: List the Number of Children and Number of Families
First, let's restate the data given in the table:
- 45 families have 0 children
- 32 families have 1 child
- 19 families have 2 children
- 8 families have 3 children
- 6 families have 4 children
### Step 2: Expand the Data
We will now expand this data into a list where we replicate each number of children by the number of families.
- 45 families 0 children = [tex]\( [0, 0, 0, \ldots, 0] \times 45 \)[/tex] (45 zeros)
- 32 families 1 child = [tex]\( [1, 1, 1, \ldots, 1] \times 32 \)[/tex] (32 ones)
- 19 families 2 children = [tex]\( [2, 2, 2, \ldots, 2] \times 19 \)[/tex] (19 twos)
- 8 families 3 children = [tex]\( [3, 3, 3, \ldots, 3] \times 8 \)[/tex] (8 threes)
- 6 families * 4 children = [tex]\( [4, 4, 4, \ldots, 4] \times 6 \)[/tex] (6 fours)
Combining all these lists into a single list gives us a complete dataset of number of children across 110 families.
### Step 3: Sort the List (Already Ordered)
The list of children per family, when combined, would look like this:
[tex]\[ [0, 0, \ldots, 0, 1, 1, \ldots, 1, 2, 2, \ldots, 2, 3, 3, \ldots, 3, 4, 4, \ldots, 4] \][/tex]
Since the original sets were already ordered, this combined list will be:
[tex]\[ [0, 0, \ldots, 0, 1, 1, \ldots, 1, 2, 2, \ldots, 2, 3, 3, \ldots, 3, 4, 4, \ldots, 4] \][/tex]
### Step 4: Find the Median
To find the median, we need to determine the middle value in the ordered list. Since there are 110 data points, the median will be the average of the 55th and 56th elements in the list.
- The first 45 numbers in the list are 0.
- The next 32 numbers in the list are 1.
Thus, the 55th and 56th numbers in the list fall within the 1s.
### Step 5: Calculate the Median
Since both the 55th and 56th elements are 1, the median number of children is:
[tex]\[ \text{Median} = \frac{1 + 1}{2} = 1.0 \][/tex]
### Final Answer
The median number of children in these families is [tex]\( 1.0 \)[/tex].
