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JEE Main 20207 JanuaryEvening Shift
Exam
JEE Main
Year
2020
Date
7 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Statistics

JEE Main 2020 · 7 January · Evening Shift · Mathematics · Statistics

If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x...

If the mean and variance of eight numbers 3,7,9,12,13,20,x3, 7, 9, 12, 13, 20, x and yy be 1010 and 2525 respectively, then x⋅yx \cdot y is equal to

Correct answer

0

Step-by-step solution

Mean =x−=3+7+9+12+13+20+x+y8=10⇒x+y=16…(i)= \overset{-}{x} = \dfrac{3 + 7 + 9 + 12 + 13 + 20 + x + y}{8} = 10 ⇒ x + y = 16 \ldots \left(i\right)
Variance σ2=∑(xi)28−(x−)2=25{\sigma}^{2} = \dfrac{∑ {\left({x}_{i}\right)}^{2}}{8} - {\left(\overset{-}{x}\right)}^{2} = 25
9+49+81+144+169+400+x2+y28−100=25\dfrac{9 + 49 + 81 + 144 + 169 + 400 + {x}^{2} + {y}^{2}}{8} - 100 = 25
⇒x2+y2=148…(ii)⇒ {x}^{2} + {y}^{2} = 148 \ldots \left(ii\right)
(x+y)2=(16)2=x2+y2+2xy=256⇒xy=54{\left(x + y\right)}^{2} = {\left(16\right)}^{2} = {x}^{2} + {y}^{2} + 2xy = 256 ⇒ xy = 54
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