The average of the sequence 100, 200, 300, ..., 1000 is 550. If each term is divided by 5, what is the new average?

Introduction / Context:
Transformations applied uniformly to every term in a data set apply the same transformation to the average. This property lets us compute new averages quickly without re-summing all terms.

Given Data / Assumptions:

• Original sequence: 100, 200, 300, ..., 1000 (step 100)
• Original average = 550
• Operation: divide each term by 5

Concept / Approach:
If each data point is divided by a constant k, the average is also divided by k. Thus New average = Old average / 5.

Step-by-Step Solution:

Verification / Alternative check:
New sequence becomes 20, 40, 60, ..., 200. The first and last terms’ mean is (20 + 200) / 2 = 110, matching the transformation rule.

Why Other Options Are Wrong:

• 450: Incorrect scaling; seems like subtracting 100 instead of dividing.
• 45 and 55: Both reflect order-of-magnitude mistakes.
• None of these: Correct, since the true new average 110 is not listed among the numeric options.

Common Pitfalls:
Confusing division with subtraction, or mistakenly dividing by the number of terms again after transformation.

Final Answer:
None of these (the correct new average is 110).