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13.Statistics
hard
निम्नलिखित आँकड़ों के लिए माध्य व प्रसरण ज्ञात कीजिए।
| ${x_i}$ | $92$ | $93$ | $97$ | $98$ | $102$ | $104$ | $109$ |
| ${f_i}$ | $3$ | $2$ | $3$ | $2$ | $6$ | $3$ | $3$ |
A
$29.09$
B
$29.09$
C
$29.09$
D
$29.09$
Solution
The data is obtained in tabular form as follows.
| ${x_i}$ | ${f_i}$ | ${f_i}{x_i}$ | ${{x_i} – \bar x}$ | ${\left( {{x_i} – \bar x} \right)^2}$ | ${f_i}{\left( {{x_i} – \bar x} \right)^2}$ |
| $92$ | $3$ | $276$ | $-8$ | $64$ | $192$ |
| $93$ | $2$ | $186$ | $-7$ | $49$ | $98$ |
| $97$ | $3$ | $291$ | $-3$ | $9$ | $27$ |
| $98$ | $2$ | $196$ | $-2$ | $4$ | $8$ |
| $102$ | $6$ | $612$ | $2$ | $4$ | $24$ |
| $104$ | $3$ | $312$ | $4$ | $16$ | $48$ |
| $109$ | $3$ | $327$ | $9$ | $81$ | $243$ |
| $22$ | $2200$ | $640$ |
Here, $N = 22,\sum\limits_{i = 1}^7 {{f_i}{x_i}} = 2200$
$\therefore \bar x = \frac{1}{n}\sum\limits_{i = 1}^7 {{f_i}{x_i}} = \frac{1}{{22}} \times 2200 = 100$
Variance $\left( {{\sigma ^2}} \right) = \frac{1}{N}\sum\limits_{i = 1}^7 {{f_i}{{\left( {{x_i} – \bar x} \right)}^2} = } \frac{1}{{22}} \times 640 = 29.09$
Standard 11
Mathematics
Similar Questions
निम्नलिखित आँकड़ों से बताइए कि $A$ या $B$ में से किस में अधिक बिखराव है
| अंक | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ | $60-70$ | $70-80$ |
| समूह $A$ | $9$ | $17$ | $32$ | $33$ | $40$ | $10$ | $9$ |
| समूह $B$ | $10$ | $20$ | $30$ | $25$ | $43$ | $15$ | $7$ |
hard
