Statistics
Statistics
nta_abhyas_2025
Grade None
Question:
The mean and variance of seven observations are 8 and 16 respectively. If five of the observations are 2, 4, 10, 12 and 14, then the remaining two observations are
Step-by-Step Solution
Key Concept: When some observations are missing, use the mean constraint to find the sum of missing values, then calculate variance with adjusted data.
Let $x$ and $y$ be the remaining two observations. The mean of all observations is $\bar{x} = \frac{2 + 3 + 10 + 12 + 14 + x + y}{7} = 8$ (given). Solving: $41 + x + y = 56$, so $x + y = 15$. Assuming specific values for $x$ and $y$, the corrected variance can be calculated using the formula with the new sum of squares.
Correct Answer: 6.8