Central Tendency & DispersionPYQ Jun 23Question 3142 of 473
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If the Standard Deviation of data 2,4,5,6,8,17\displaystyle 2, 4, 5, 6, 8, 17 is 4.47\displaystyle 4.47, then Standard Deviation of the data 4,8,10,12,16,34\displaystyle 4, 8, 10, 12, 16, 34 is

Options

A8.94\displaystyle 8.94
B2.24\displaystyle 2.24
C13.41\displaystyle 13.41
D1.24\displaystyle 1.24
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Correct Answer

✅ Option a — 8.94\displaystyle 8.94

All Options:

  • A8.94\displaystyle 8.94
  • B2.24\displaystyle 2.24
  • C13.41\displaystyle 13.41
  • D1.24\displaystyle 1.24

Detailed Solution & Explanation

**Given:** SD of {2,4,5,6,8,17}=4.47\displaystyle \{2, 4, 5, 6, 8, 17\} = 4.47 **Observation:** The second dataset {4,8,10,12,16,34}\displaystyle \{4, 8, 10, 12, 16, 34\} is obtained by multiplying each element of the first dataset by 2: 4=2×2,8=2×4,10=2×5,12=2×6,16=2×8,34=2×174 = 2 \times 2, \quad 8 = 2 \times 4, \quad 10 = 2 \times 5, \quad 12 = 2 \times 6, \quad 16 = 2 \times 8, \quad 34 = 2 \times 17 **Key Property:** When every observation is multiplied by a constant k\displaystyle k, the SD also gets multiplied by ∣k∣\displaystyle |k|: SDnew=∣k∣×SDoldSD_{new} = |k| \times SD_{old} **Step 1:** Here k=2\displaystyle k = 2. SDnew=2×4.47=8.94SD_{new} = 2 \times 4.47 = 8.94 Hence, **Option A** is the correct answer.

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