- Home
- Standard 11
- Mathematics
सात प्रेक्षणों के माध्य तथा प्रसरण क्रमशः $8$ तथा $16$ है। यदि इनमें से $5$ प्रेक्षण $2,4,10,12,14$ है, तो शेष दो प्रेक्षणों का गुणनफल है
$40$
$45$
$49$
$48$
Solution
Let $7$ observation be ${x_1},{x_2},{x_3},{x_4},{x_5},{x_6},{x_7}$
$\bar x = 8 \Rightarrow \sum\limits_{i = 1}^7 {{x_i}} = 56\,\,\,\,\,\,…….\left( 1 \right)$
Also ${\sigma ^2} = 16$
$ \Rightarrow 16 = \frac{1}{7}\left( {\sum\limits_{i = 1}^7 {x_i^2} } \right) – {\left( {\bar x} \right)^2}$
$ \Rightarrow 16 = \frac{1}{7}\left( {\sum\limits_{i = 1}^7 {x_i^2} } \right) – 64$
$ \Rightarrow \left( {\sum\limits_{i = 1}^7 {x_i^2} } \right) = 560\,\,\,\,\,\,\,\,\,…….\left( 2 \right)$
Now, ${x_1} = 2,{x_2} = 4,{x_3} = 10,{x_4} = 12,{x_5} = 14$
$ \Rightarrow {x_6} + {x_7} = 14$ (from $(1)$) and $x_6^2 + x_7^2 = 100$ (from$(2)$)
$\therefore x_6^2 + x_7^2 = {\left( {{x_6} + {x_7}} \right)^2} – 2{x_6}{x_7} \Rightarrow {x_6}{x_7} = 48$
Similar Questions
निम्नलिखित बंटन के लिए माध्य, प्रसरण व मानक विचलन ज्ञात कीजिए
| वर्ग | $30-40$ | $40-50$ | $50-60$ | $60-70$ | $70-80$ | $80-90$ | $90-100$ |
| बारंबारता | $3$ | $7$ | $12$ | $15$ | $8$ | $3$ | $2$ |
