A) \[\frac{9}{8}\]
B) \[2\]
C) \[\frac{7}{8}\]
D) \[1\]
Correct Answer: D
Solution :
Mean of the date 7, 8, 9, 7, 8, 7 \[\lambda \], 8 is 8 \[\therefore M=\frac{7+8+9+7+8+7+\lambda +8}{8}=8\] \[\Rightarrow \frac{54+\lambda }{8}=8\] \[\Rightarrow \lambda =10\] Now, variance \[{{\sigma }^{2}}\] is the average of squared difference from mean So, \[{{\sigma }^{2}}=\frac{{{(7-8)}^{2}}+{{(8-8)}^{2}}+{{(9-8)}^{2}}+{{(7-8)}^{2}}+{{(8-8)}^{2}}+{{(7-8)}^{2}}+{{(10-8)}^{2}}+{{(8-8)}^{2}}}{8}\] \[=\frac{1+0+1+1+0+1+4+0}{8}=\frac{8}{8}=1\] Hence, the variance is 1.
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