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The heights (in cm) of 40 students are grouped as follows: Class interval | Frequency 140‑149 | 5 150‑159 | 12 160‑169 | 15 170‑179 | 6 180‑189 | 2 Find the estimated mean height.

medium 2 marks Class 10 · Mathematics · Statistics
Answer
Estimated mean height = 161.5 cm

The correct answer is Estimated mean height = 161.5 cm — Thus the estimated mean height is 161.5 cm.

Step-by-step solution

  1. Compute the midpoint of each class: 144.5, 154.5, 164.5, 174.5, 184.5.
  2. Multiply each midpoint by its frequency: 144.5×5 = 722.5 154.5×12 = 1854 164.5×15 = 2467.5 174.5×6 = 1047 184.5×2 = 369
  3. Add these products: 722.5+1854+2467.5+1047+369 = 6460.
  4. Divide by total frequency (40): 6460 ÷ 40 = 161.5.
  5. Thus the estimated mean height is 161.5 cm.
Common mistake: Using class limits instead of class midpoints for calculation

Concept tested: Mean of grouped data

Published · How this solution was prepared and checked

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