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13.Statistics
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आंकडों
| $x_i$ | $0$ | $1$ | $5$ | $6$ | $10$ | $12$ | $17$ |
| $f_i$ | $3$ | $2$ | $3$ | $2$ | $6$ | $3$ | $3$ |
का प्रसरण $\sigma^2$ बराबर है ..........
A
$28$
B
$29$
C
$27$
D
$25$
(JEE MAIN-2024)
Solution
| $x_i$ | $f_i$ | $f_ix_i$ | $f_ix_i^2$ |
| $0$ | $3$ | $0$ | $0$ |
| $1$ | $2$ | $2$ | $2$ |
| $5$ | $3$ | $15$ | $75$ |
| $6$ | $2$ | $12$ | $72$ |
| $10$ | $6$ | $60$ | $600$ |
| $12$ | $3$ | $36$ | $432$ |
| $17$ | $3$ | $51$ | $867$ |
|
$\sum f_i = 22$ |
$\sum f_ix_i^2 = 2048$ |
$ \therefore \quad \sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}=176$
$ \text { So } \overline{\mathrm{x}}=\frac{\sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum \mathrm{f}_{\mathrm{i}}}=\frac{176}{22}=8 $
$ \text { for } \sigma^2=\frac{1}{\mathrm{~N}} \sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}^2-(\overline{\mathrm{x}})^2 $
$ \quad=\frac{1}{22} \times 2048-(8)^2$
$ \quad=93.090964 $
$\quad=29.0909$
Standard 11
Mathematics
Similar Questions
यदि निम्न बारंबारता बंटन :का प्रसरण $50$ है, तो $x$ का मान है |
| वर्ग | $10-20$ | $20-30$ | $30-40$ |
| बारंबारता | $2$ | $x$ | $2$ |
यदि बारंबारता बंटन
| $x_i$ | $2$ | $4$ | $6$ | $8$ | $10$ | $12$ | $14$ | $16$ |
| $f_i$ | $4$ | $4$ | $\alpha$ | $15$ | $8$ | $\beta$ | $4$ | $5$ |
के माध्य तथा प्रसरण क्रमशः $9$ तथा $15.08$ हैं, तो $\alpha^2+\beta^2-\alpha \beta$ का मान है________________
