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13.Statistics
hard
यदि पाँच प्रे क्षणों $x _{1}, x _{2}, x _{3}, x _{4}, x _{5}$ का माध्य तथा मानक विचलन क्रमशः $10$ तथा $3$ हो, तो छः प्रेक्षणों $x _{1}, x _{2}, \ldots, x _{5}$ तथा $-50$ का प्रसरण होगा-
A
$509.5$
B
$586.5$
C
$582.5$
D
$507.5$
(JEE MAIN-2019)
Solution
$\sum {x = 50} $
${\left( 3 \right)^2} = \frac{1}{5}\left( {e{x^2} – \frac{{{{\left( {ex} \right)}^2}}}{5}} \right)$
$9 = \frac{1}{5}\left( {\sum {{x^2} – \frac{{2500}}{5}} } \right)$
$\therefore \sum {{x^2} = 545} $
New variable $ = \frac{1}{6}\left( {3045 – \frac{0}{6}} \right) = 507.5$
Standard 11
Mathematics
