Question

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Answer 1

Answer:

$\sf \: {\displaystyle\textstyle\sum}$ (xᵢ – 3) = 170

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$\sf \: {x_1}– 3 + x₂ – 3 + x₃ – 3t ... xₙ – 3 = 170 x₁ + x₂ + ... + xₙ = 170 + 3ₙ --- equation 1$

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${\displaystyle\textstyle\sum}$ (xᵢ – 6) = 50

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$\sf \: x₁ + x₂ + ... + xₙ = 50 + 6n --- quation 2.$

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$\sf \: From \: equation \: 1 \: and \: equation \: 2, \: we \: get \:$

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$\sf \: 170 + 3n = 50 + 6n = 50 + 6n$

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⇒ $\sf \: 170 \: – 50 = 6n – 3n$

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⇒ $\sf \: 3n = 120$

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⇒ $\sf \: n = 40$

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$\sf \: Value \: of \: n \: = 40$

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$\sf \: Now \: mean \: = (x₁ \: + x₂ \: + \: ... + \: xₙ)/n$

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$\sf \: Putting \: value \: of \: n \: = 40, \: we \: get$

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$\sf \: {50 \: + \: 6(40)}/40 = (50 \: + 2\: 40)/40 = 290/40 = 7.25$

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$\sf \: Mean \: = \: 7.25$

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Therefore, value of n = 40 and the mean of n values is 7.25