Question
The means of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6, then the other two are:
Answer: Option C
:
C
¯x=4,N=5and∑(x−¯x2)N=5.2⇒∑(x−¯x)2=(5.2)5∴∑(x−¯x)2=26∴(1−4)2+(2−4)2+(6−4)2+(α−4)2+(β−4)2=26∴(α−4)2+(β−4)2=9Also,1+2+6+α+β5=4∴α+β=20−9=11Clearly 4, 7 only satisfy the above equation inα,β.Hence required numbers are 4, 7.
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:
C
¯x=4,N=5and∑(x−¯x2)N=5.2⇒∑(x−¯x)2=(5.2)5∴∑(x−¯x)2=26∴(1−4)2+(2−4)2+(6−4)2+(α−4)2+(β−4)2=26∴(α−4)2+(β−4)2=9Also,1+2+6+α+β5=4∴α+β=20−9=11Clearly 4, 7 only satisfy the above equation inα,β.Hence required numbers are 4, 7.
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