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NDA 1 2025 Maths, question 113

Topic: Statistics

Q113

The arithmetic mean of 100 observations is 50. If 5 is subtracted from each observation and then divided by 20, then what is the new arithmetic mean?

  1. (a) 2.25Correct answer
  2. (b) 3.5
  3. (c) 4.25
  4. (d) 5.5

Solution.

Answer: (a) 2.25

  1. Means transform linearly.
  2. For Y=(X−5)/20Y = (X - 5)/20, Yˉ=(Xˉ−5)/20=(50−5)/20=2.25\bar{Y} = \left( \bar{X} - 5 \right)/20 = (50 - 5)/20 = 2.25.