Six families in Indira Nagar have 7, 8, 10, 13, 6, and 10 members. If 1 member from each family moves to a hostel, what is the new average family size?

Introduction / Context:
When the same increment or decrement is applied to each group in a collection, the effect on the overall average is straightforward. Here, one member leaves each family, reducing each family's size by 1.

Given Data / Assumptions:

• Original sizes: 7, 8, 10, 13, 6, 10
• Six families total
• One member leaves each family

Concept / Approach:
Subtract 1 from each family, sum the new sizes, and divide by 6. Alternatively, compute the original average and then subtract 1 directly from the average (since all groups change equally).

Step-by-Step Solution:

Verification / Alternative check:
Original average = 54 / 6 = 9. Decreasing each family by 1 reduces the average by 1 ⇒ 9 - 1 = 8. Matches the computed value.

Why Other Options Are Wrong:

• 9: That was the original average, not the new one.
• 10 and 13: Both exceed the feasible mean after uniform reduction.
• None of these: A correct option exists (8).

Common Pitfalls:
Subtracting only 1 in total rather than 1 per family (which would undercount the reduction).

Final Answer:
8