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NDA 1 2025 Maths, question 120

Topic: Statistics

Q120

What is the arithmetic mean of 82,92,102,…,1528^{2},9^{2},10^{2},\ldots,15^{2}?

  1. (a) 133.5
  2. (b) 135.5
  3. (c) 137.5Correct answer
  4. (d) 139.5

Solution.

Answer: (c) 137.5

  1. There are eight terms.
  2. Their sum is ∑j=115j2−∑j=17j2=15⋅16⋅316−7⋅8⋅156=1240−140=1100\sum_{j = 1}^{15}j^{2} - \sum_{j = 1}^{7}j^{2} = \frac{15 \cdot 16 \cdot 31}{6} - \frac{7 \cdot 8 \cdot 15}{6} = 1240 - 140 = 1100.
  3. The mean is 1100/8=137.51100/8 = 137.5.