Find the variance of the given numbers: 36, 28, 45, and 51.

  1. 63.5
  2. 68.5
  3. 71.5
  4. 76.5

Answer (Detailed Solution Below)

Option 4 : 76.5
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Detailed Solution

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Mean is the average of the given numbers,

⇒ Mean = (36 + 28 + 45 + 51)/4 = 160/4 = 40

Variance is calculated by taking the average of the squares of the difference between each term and the mean,

⇒ Variance = [(36 - 40)2 + (28 - 40)2 + (45 - 40)2 + (51 - 40)2]/4

= [16 + 144 + 25 + 121]/4 = 306/4 = 76.5

∴ Variance of the given numbers = 76.5
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