Statistics
Mean Deviation and Variance — Finding 2a+b−c
nta_pyq_2024_apr
Grade 11
Question:
Let $a,b,c\in\mathbb{N}$ and $a<b<c$. Let the mean, the mean deviation about the mean and the variance of the 5 observations $9,25,a,b,c$ be 18, 4 and $\dfrac{136}{5}$, respectively. Then $2a+b-c$ is equal to _____
Step-by-Step Solution
Key Concept: Mean $=18\Rightarrow a+b+c=56$. Mean deviation $=4\Rightarrow|18-9|+|18-25|+|18-a|+|18-b|+|18-c|=20\Rightarrow|18-a|+|18-b|+|18-c|=4$. Variance $\Rightarrow(18-a)^2+(18-b)^2+(18-c)^2=6$.
$a=17,b=19,c=20$. $2a+b-c=33$.
Correct Answer: 33