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AP EAMCET · Maths · Statistics

Let \(a\) and \(b\) be two real numbers. If the arithmetic mean and the variance of \(a, b, 8,5\) and 10 are respectively 6 and 6.8 then an ordered pair \((a, b)=\)

  1. A \((3,4)\)
  2. B \((1,6)\)
  3. C \((7,0)\)
  4. D \((-2,9)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \((3,4)\)

Step-by-step Solution

Detailed explanation

\( \bar{x} = \frac{\sum x_i}{n} \) \( 6 = \frac{a+b+8+5+10}{5} \) \( 30 = a+b+23 \) \( a+b=7 \) \( \sigma^2 = \frac{\sum x_i^2}{n} - (\bar{x})^2 \) \( 6.8 = \frac{a^2+b^2+8^2+5^2+10^2}{5} - 6^2 \) \( 6.8+36 = \frac{a^2+b^2+64+25+100}{5} \) \( 42.8 \times 5 = a^2+b^2+189 \)…