- Home
- Standard 11
- Mathematics
13.Statistics
hard
निम्नलिखित बारंबारता बंटन के लिए माध्य व प्रसरण ज्ञात कीजिए।
| वर्ग | $0-30$ | $30-60$ | $60-90$ | $90-120$ | $120-150$ | $50-180$ | $180-210$ |
| बारंबारता | $2$ | $3$ | $5$ | $10$ | $3$ | $5$ | $2$ |
A
$2276$
B
$2276$
C
$2276$
D
$2276$
Solution
| Class |
Frequency ${f_i}$ |
Mid-point ${x_i}$ |
${y_i} = \frac{{{x_i} – 105}}{{30}}$ | ${y_i}^2$ | ${f_i}{y_i}$ | ${f_i}{y_i}^2$ |
| $0-30$ | $2$ | $15$ | $-3$ | $9$ | $-6$ | $18$ |
| $30-60$ | $3$ | $45$ | $-2$ | $4$ | $-6$ | $12$ |
| $60-90$ | $5$ | $75$ | $-1$ | $1$ | $-5$ | $5$ |
| $90-120$ | $10$ | $105$ | $0$ | $0$ | $0$ | $0$ |
| $120-150$ | $3$ | $135$ | $1$ | $1$ | $3$ | $3$ |
| $150-180$ | $5$ | $165$ | $2$ | $4$ | $10$ | $20$ |
| $180-210$ | $2$ | $195$ | $3$ | $9$ | $6$ | $18$ |
| $30$ | $2$ | $76$ |
Mean, $ \bar x = A + \frac{{\sum\limits_{i = 1}^7 {{f_i}{y_i}} }}{N} \times h$
$ = 105 + \frac{2}{{30}} \times 30 = 105 + 2 = 107$
Variance, $\left( {{\sigma ^2}} \right) = \frac{{{h^2}}}{{{N^2}}}\left[ {N\sum\limits_{i = 1}^7 {{f_i}{y_i}^2 – {{\left( {\sum\limits_{i = 1}^7 {{f_i}{y_i}} } \right)}^2}} } \right]$
$=\frac{(30)^{2}}{(30)^{2}}\left[30 \times 76-(2)^{2}\right]$
$=2280-4$
$=2276$
Standard 11
Mathematics
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 | $3$ | $7$ | $12$ | $15$ | $8$ | $3$ | $2$ |
hard
