Before moving to the next chapter, confirm you can do each of the following without referring back to your notes:

State the formula for the average of first n natural numbers, first n even numbers, and first n odd numbers — without mixing them up.
Derive the average of any consecutive AP using only its first and last terms, even when it doesn’t start from 1.
Recall the average-of-squares and average-of-cubes formulas for the first n natural numbers, and recognise the identity that sum of cubes equals the square of the sum.
Distinguish instantly between a “replacement” scenario (group size fixed) and a “join/leave” scenario (group size changes), and apply the correct formula variant for each.
Decide, within 2 seconds of reading an average-speed question, whether distances or times are equal, and apply 2xy/(x+y) or the simple mean accordingly.
Compute a weighted average or a combined-group average using both the direct fraction method and the faster alligation (ratio-split) method, and get the same answer both ways.
Handle an average-age question involving a birth, marriage, or departure during the elapsed time period, without incorrectly shifting every member’s age by the same amount.
Use the deviation (assumed mean) method to calculate an average of large or awkward numbers quickly, and use the zero-sum property of true deviations to self-verify a “find the missing value” answer.

If you can confidently tick off all eight points above, you are fully prepared for any Average question that SSC CGL, CHSL, MTS, or RRB NTPC/Group D can present. Revisit Sections 3 and 4 periodically — the Shortcuts and Common Mistakes lists are meant to be re-read the night before your exam as a final refresher, not just studied once.

End of Chapter 7: Average. In the next chapter, continue with Ratio & Proportion, which extends the weighted-average and alligation ideas introduced here into a full standalone framework.