Statistics
Mean and variance of units digits of perfect squares
MJAT_TS6_P2
Grade 12
Question:
The units digits of $1^2,2^2,\ldots,2025^2$ cycle with period 10: $\{1,4,9,6,5,6,9,4,1,0\}$. If $p$=arithmetic mean, $q$=variance, then $[K]$ where $K=(p+q)^2+(p-q)^2$ equals:
Step-by-Step Solution
Key Concept: $K=(p+q)^2+(p-q)^2=2(p^2+q^2)$. Compute $p$ and $q$ from the periodic sequence of 2025 terms.
$[K]=\mathbf{58}$.
Correct Answer: 58