Question
Download Solution PDFপাচঁটি ধারাবাহিক জোড় সংখ্যার গড় হল 16, সংখ্যা গুলির ভেদমান (ভেরিএন্স) কত হবে?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত :
পাচঁটি ধারাবাহিক জোড় সংখ্যার গড় = 16
অনুসৃত সূত্র :
\({\rm{গড় \;}}\left( {\rm{m}} \right) = \;\frac{{\left\{ {2{\rm{a\;}} + \left( {{\rm{n\;}} - 1} \right){\rm{d}}} \right\}}}{2}\)
V =ভেদমান
∑ = সমষ্টি
x = পর্যবেক্ষণ
n = পর্যবেক্ষণের সংখ্যা
a = সংখ্যা গুলির 1ম পদ (টার্ম)
d = সাধারণ অন্তর
গণনা :
\(\frac{{\left\{ {2{\rm{a\;}} + \left( {{\rm{n\;}} - 1} \right){\rm{d}}} \right\}}}{2} = 16\)
⇒ 2a + (5 – 1)2 = 32
⇒ 2a + 4 × 2 = 32
⇒ 2a = 32 – 8
⇒ 2a = 24
⇒ a = 12
1ম পদ = 12
অন্যান্য পদগুলি হল 14, 16, 18, 20
\({\rm{V}} = {\rm{\;}}\frac{{{{\left( {12{\rm{\;}} - 16} \right)}^2} + {{\left( {14{\rm{\;}} - 16} \right)}^2} + {{\left( {16{\rm{\;}} - 16} \right)}^2} + {{\left( {18{\rm{\;}} - 16} \right)}^2} + {{\left( {20{\rm{\;}} - 16} \right)}^2}}}{5}\)
⇒ \({\rm{\;}}\frac{{16{\rm{\;}} + {\rm{\;}}4{\rm{\;}} + {\rm{\;}}0{\rm{\;}} + {\rm{\;}}4{\rm{\;}} + 16}}{5}\)
⇒ \({\rm{\;}}\frac{{40}}{5}\)
⇒ 8
⇒ V = 8
∴ সংখ্যাগুলির ভেদমান হল 8
Last updated on Jun 25, 2025
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