The following table gives the number of children of 10 families in a village. Find the average number of children per family.

Steps to Solve

1. Calculate the Total Number of Families

Add the number of families for all categories of children.

[ \text{Total Families} = 10 + 21 + 55 + 42 + 15 + 7 = 150 ]

2. Calculate the Total Number of Children

Multiply the number of children by the number of families for each category and then sum all these values.

[ \text{Total Children} = (0 \times 10) + (1 \times 21) + (2 \times 55) + (3 \times 42) + (4 \times 15) + (5 \times 7) ]

Calculating this step-by-step:

• For 0 children: (0 \times 10 = 0)
• For 1 child: (1 \times 21 = 21)
• For 2 children: (2 \times 55 = 110)
• For 3 children: (3 \times 42 = 126)
• For 4 children: (4 \times 15 = 60)
• For 5 children: (5 \times 7 = 35)

Now sum these values:

[ \text{Total Children} = 0 + 21 + 110 + 126 + 60 + 35 = 352 ]

3. Calculate the Average Number of Children Per Family

Use the formula for average:

[ \text{Average} = \frac{\text{Total Children}}{\text{Total Families}} = \frac{352}{150} ]

4. Final Calculation

Now, perform the division:

[ \text{Average} \approx 2.347 \text{ (rounded to three decimal places)} ]