Central Tendency & DispersionPYQ Nov. 19Question 3129 of 473
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SD from numbers 1,4,5,7,8\displaystyle 1, 4, 5, 7, 8 is 2.45\displaystyle 2.45. If 10\displaystyle 10 is added to each then SD will be:

Options

A12.45\displaystyle 12.45
B24.5\displaystyle 24.5
C12\displaystyle 12
DWill not change
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Correct Answer

✅ Option d — Will not change

All Options:

  • A12.45\displaystyle 12.45
  • B24.5\displaystyle 24.5
  • C12\displaystyle 12
  • DWill not change

Detailed Solution & Explanation

**Concept:** Standard Deviation is independent of a change of origin (i.e., adding or subtracting a constant from all observations). **Reason:** When a constant c\displaystyle c is added to every observation, the new observation xi′=xi+c\displaystyle x_i' = x_i + c. The new mean xˉ′=xˉ+c\displaystyle \bar{x}' = \bar{x} + c. The deviation from the new mean: xi′−xˉ′=(xi+c)−(xˉ+c)=xi−xˉx_i' - \bar{x}' = (x_i + c) - (\bar{x} + c) = x_i - \bar{x} The deviations remain unchanged, hence the Standard Deviation remains unchanged. **Given:** SD of {1,4,5,7,8}\displaystyle \{1, 4, 5, 7, 8\} = 2.45. When 10 is added to each observation, the new data set is {11,14,15,17,18}\displaystyle \{11, 14, 15, 17, 18\}. The SD of the new data set = SD of original data set = **2.45** (unchanged). Hence, **Option D** is the correct answer.

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