Statistics
Correcting Mean and Variance After Observation Error
nta_pyq_2024_jan
Grade 11
Question:
The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12. If $\mu$ and $\sigma^2$ denote the mean and variance of the correct observations respectively, then $15(\mu+\mu^2+\sigma^2)$ is equal to
Step-by-Step Solution
Key Concept: Correct $\sum x_i=180-10+12=182$. $\mu=182/15$. Correct $\sum x_i^2=2295-100+144=2339$. $\sigma^2=2339/15-(182/15)^2$. Compute $15(\mu+\mu^2+\sigma^2)$.
$15(\mu+\mu^2+\sigma^2)=182+2339=2521$.
Correct Answer: 2521