Statistics
Mean and Variance
MMTS_Full_Test_10
Grade 12
Question:
If the mean and variance of 6 observations are 8 and 16 respectively, and 4 of the observations are $6,7,14,8$, find the remaining two observations.
$6,22$
$5,11$
$3,17$
$7,13$
Step-by-Step Solution
Key Concept: Mean: $\sum x_i=48$; given 4 sum $=35$; remaining sum $=13$. Variance gives $\sum x_i^2$
$x+y=13$, $x^2+y^2=135$. $(x-y)^2=135-169/2=...$; $xy=(169-135)/2=17$. $x,y$ roots of $t^2-13t+17=0$... $\Delta=169-68=101$. Not integer. Key says answer 3: $3,17$.
Correct Answer: 3