Statistics
Mean and Variance — Mean of Derived Numbers
nta_pyq_2026_jan
Grade 11
Question:
Let the mean and variance of 8 numbers $-10,-7,-1,x,y,9,2,16$ be $\dfrac{7}{2}$ and $\dfrac{293}{4}$, respectively. Then the mean of 4 numbers $x,y,x+y+1,|x-y|$ is:
Step-by-Step Solution
Key Concept: Mean $=\tfrac{7}{2}$: sum $=28\Rightarrow x+y=19$. Variance: $\tfrac{\sum x_i^2}{8}-\tfrac{49}{4}=\tfrac{293}{4}\Rightarrow\sum x_i^2=684$. Known: $100+49+1+81+4+256=491$, so $x^2+y^2=193$.
Mean $=11$.
Correct Answer: 1