The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers is 20.
The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers is 20. Find the excluded number.
Let the numbers be x1, x2,..., x6.
Mean = 23
We know:
Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$
Thus, we have:
$23=\frac{x_{1}+x_{2}+\ldots+x_{6}}{6}$
$x_{1}+x_{2} \ldots \ldots \ldots x_{6}=138$
If one number, say, x6, is excluded, then we have:
$20=\frac{x_{1}+x_{2}+\ldots+x_{5}}{5}$
$x_{1}+x_{2} \ldots \ldots+x_{5}=100 \ldots \ldots \ldots \ldots \ldots \ldots$ (ii)
Using (i) and (ii), we get:
$138=x_{1}+x_{2}+\ldots+x_{5}+x_{6}$
$\Rightarrow 138=100+x_{6} \quad \ldots$ (i)
$\Rightarrow x_{6}=38$
Thus, the excluded number is 38
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.