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જો $\sum\limits_{i\, = \,1}^{18} {({x_i}\, - \,\,8)\,\, = \,\,9} $ અને $\,\sum\limits_{i\, = \,1}^{18} {{{({x_i}\, - \,\,8)}^2}\, = \,\,45} ,\,$ હોય, તો $\,{{\text{x}}_{\text{1}}},\,\,{x_2},\,........\,\,{x_{18}}$ નું પ્રમાણિત વિચલન શોધો .
A
$3/4$
B
$5/2$
C
$1/2$
D
$3/2$
Solution
ધારો કે $\,\Sigma\,({x_i}\, – \,\,8)\,\, = \,\,{d_i}$
$\therefore \,\,{\sigma _x}\,\, = \,\,{\sigma _d}\,\,\,\, = \,\sqrt {\frac{{\Sigma d_i^2}}{n}\,\, – \,\,{{\left( {\frac{{\Sigma {d_i}}}{n}} \right)}^2}} \,\,\,\,$
$\, = \,\,\sqrt {\frac{{45}}{{18}}\,\, – \,\,{{\left( {\frac{9}{{18}}} \right)}^2}} \,\,\,\,\, = \,\,\sqrt {\frac{5}{2}\,\, – \,\,\frac{1}{4}} \,\,\,\,\,\, = \,\,\frac{3}{2}$
Standard 11
Mathematics
Similar Questions
જો આવૃત્તિ વિતરણ
| $X_i$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
| Frequency $f_i$ | $3$ | $6$ | $16$ | $\alpha$ | $9$ | $5$ | $6$ |
નું વિચરણ $3$ હોય, તો $\alpha=…………..$
