Statistics
Mean and Variance — Finding α²+β²
nta_pyq_2024_jan
Grade 11
Question:
If the mean and variance of the data $65,68,58,44,48,45,60,\alpha,\beta,60$ where $\alpha>\beta$ are 56 and 66.2 respectively, then $\alpha^2+\beta^2$ is equal to
Step-by-Step Solution
Key Concept: Mean $=56$: $\sum x_i=560$. $(65+68+58+44+48+45+60+60)+\alpha+\beta=560\Rightarrow\alpha+\beta=112$. Variance: $\frac{\sum x_i^2}{10}-56^2=66.2\Rightarrow\sum x_i^2=31,962+\alpha^2+\beta^2$... compute $\alpha^2+\beta^2$.
$\alpha^2+\beta^2=6344$.
Correct Answer: 6344