Statistics
Missing Observations — Mean Deviation About Median
nta_pyq_2026_jan
Grade 11
Question:
The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2, 3, 5, 10, 11, 13, 15, 21, then the mean deviation about the median of all the 10 observations is
Step-by-Step Solution
Key Concept: Sum of all 10: $90$. Sum of 8 known: $80$. So $x_9+x_{10}=10$. From variance: $\sum x_i^2=10(34.2+81)=1152$. Sum of squares of 8 known: $1094$. $x_9^2+x_{10}^2=58$. Solve: $x_9x_{10}=21$, roots $t^2-10t+21=0\Rightarrow t=3$ or $7$.
Mean deviation $=5$.
Correct Answer: 3