English
Hindi
13.Statistics
hard

મધ્યસ્થ વડે $40, 62, 54, 90, 68, 76 $ અવલોકનોના સરેરાશ વિચલનનો ચલનાંક કેટલો થાય ?

A

$2.16$

B

$0.2$

C

$5$

D

આપેલ પૈકી એક પણ નહિં

Solution

આપેલા અવલોકનોને ચઢતા ક્રમમાં ગોઠવો.

$40, 54, 62, 68, 76, 90$

પદોની સંખ્યા $(n) = 6  $ (યુગ્મ)

મદયસ્થ ${\text{(M)}}\,\,\, = \,\,\,\frac{{\left( {\frac{{\text{n}}}{{\text{2}}}} \right)th\,term\,\, + \,\,\left( {\frac{n}{2}\,\, + \,\,1} \right)th\,term}}{2}\,\,\, = \,\,\frac{{62\,\, + \,\,68}}{2}\,\,\, = \,\,65$

$\Sigma \,{\text{|}}{{\text{x}}_{\text{i}}}\,{\text{ – }}\,\,{\text{M|}}\,\, = \,\,{\text{25}}\,\, + \,\,{\text{11}}\,\, + \,\,{\text{3}}\,\, + \,\,{\text{3}}\,\, + \,\,{\text{11}}\,\, + \,\,{\text{25}}\,\, = \,\,{\text{78}}$

મદયસ્થમાથી સરેરાશ વિચલન $ = \,\,\frac{{\Sigma {\text{|}}{{\text{x}}_{\text{i}}}\,{\text{ – }}\,\,{\text{M|}}}}{{\text{n}}}\,\,\, = \,\,\frac{{78}}{6}\,\,\, = \,\,13$

સરેરાશ વિચલનનો સહગુણક $ = \,\,\frac{{{\text{M}}{\text{.D}}{\text{.}}}}{{{\text{median}}}}\,\,\, = \,\,\frac{{13}}{{65}}\,\,\, = \,\,0.2$

Standard 11
Mathematics

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