Statistics
Mean and variance after omitting one observation
nta_pyq_2023_jan
Grade 11
Question:
The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and $a$ and $b$ are respectively mean and variance of remaining 6 observations, then $a + 3b - 5$ is equal to ______.
Step-by-Step Solution
Key Concept: From original: $\sum x_i = 56$, $\sum x_i^2 = 560$. After removing 14: $\sum_{6} x_i = 42$, $\sum_{6} x_i^2 = 364$. Compute new mean $a$ and variance $b$.
$a = 7$, $b = \frac{70}{6}$. $a + 3b - 5 = 7 + \frac{70}{2} - 5 = 7 + 35 - 5 = 37$.
Correct Answer: 37