Central Tendency & DispersionPYQ June 24 Series IQuestion 2938 of 473
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The Mean of a set of 20 observations on 18.3. The mean is reduced by 0.6 when a new observation is added to the set. The new observation is:

Options

A17.6
B18.0
C5.7
D24.6
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Correct Answer

✅ Option c — 5.7

All Options:

  • A17.6
  • B18.0
  • C5.7
  • D24.6

Detailed Solution & Explanation

We are given: - Number of initial observations: n1=20\displaystyle n_1 = 20 - Mean of initial observations: xˉ1=18.3\displaystyle \bar{x}_1 = 18.3 - Sum of initial observations: Sum1=20×18.3=366\displaystyle \text{Sum}_1 = 20 \times 18.3 = 366 When a new observation is added: - New number of observations: n2=21\displaystyle n_2 = 21 - The mean is reduced by 0.6\displaystyle 0.6, so the new mean is: xˉ2=18.3−0.6=17.7\displaystyle \bar{x}_2 = 18.3 - 0.6 = 17.7 - Sum of the new set of observations: Sum2=21×17.7=371.7\displaystyle \text{Sum}_2 = 21 \times 17.7 = 371.7 The value of the new observation is the difference between the new sum and the initial sum: New observation=Sum2−Sum1=371.7−366=5.7\text{New observation} = \text{Sum}_2 - \text{Sum}_1 = 371.7 - 366 = 5.7 Hence, **Option C** is the correct answer.

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