यदि 50 प्रेक्षणों x1, x2, …,x50 का माध्य और मानक विचलन दोनों 16 के बराबर हैं, तो (x1 - 4)2, (x2 - 4)2,….(x50 - 4)2 का माध्य है:

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JEE Mains Previous Paper 1 (Held On: 10 Apr 2019 Shift 2)
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  1. 400
  2. 380
  3. 525
  4. 480

Answer (Detailed Solution Below)

Option 1 : 400
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JEE Main 04 April 2024 Shift 1
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दिया गया है, 50 प्रेक्षणों का माध्य और मानक विचलन 16 के बराबर है।

माध्य, (μ)=xi50=x1+x2+.x5050=16

xi=16×50

मानक विचलन, (σ)=xi250(μ)2=16

xi250=256 x 2

अभीष्ट माध्य =(x14)2+(x24)2+(x504)250

=(xi4)250

=xi2+16×508xi50

=256×2+168×16

=528128=400
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