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If r=0.25,sumxy=45,sigma_(y)=3,sumx^(2)=50, where x and y denote deviation from their respective means, find the number of items.

Answer» <html><body><p></p>Solution :Given `: r=0.25,sumxy=<a href="https://interviewquestions.tuteehub.com/tag/45-316951" style="font-weight:bold;" target="_blank" title="Click to know more about 45">45</a>, sigma_(y)=3,sumx^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)=50` <br/> Now, ` sigma_(y)=sqrt((sumy^(2))/(N))` <br/> when `y=Y-bar(Y)` [formula of <a href="https://interviewquestions.tuteehub.com/tag/standard-632909" style="font-weight:bold;" target="_blank" title="Click to know more about STANDARD">STANDARD</a> Deviation ] <br/> `3=sqrt((sumy^(2))/(N))` <br/> Squaring both sides, we <a href="https://interviewquestions.tuteehub.com/tag/get-11812" style="font-weight:bold;" target="_blank" title="Click to know more about GET">GET</a> <br/> `9=(sumy^(2))/(N) <a href="https://interviewquestions.tuteehub.com/tag/implies-1037962" style="font-weight:bold;" target="_blank" title="Click to know more about IMPLIES">IMPLIES</a> sumy^(2)=9N` <br/> Now, `r=(sumxy)/(sqrt(sumx^(2)xxsumy^(2)))` <br/> `implies 0.25=(45)/(sqrt(50xx9N))` <br/> Squaring both sides<br/> `0.0625=((45)^(2))/(50xx9N)` <br/> `0.0625=(2,025)/(50xx9N)` <br/> `implies 0.0625=(2,025)/(450N)` <br/> `implies (0.0625)(450)N)=2,025` <br/> `implies (28.125)N=2,025` <br/> `:.N=(2,025)/(28.125)=72` <br/> Number of Items =72</body></html>


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