Statistics
Mean and Median
MMTS_Full_Test_19
Grade 12
Question:
Consider the frequency distribution: Class: $0$-$10$, $10$-$20$, $20$-$30$, $30$-$40$, $40$-$50$, $50$-$60$; Frequency: $3$, $a$, $b$, $11$, $8$, $4$. If the mean is $\frac{277}{9}$ and median is $\frac{335}{11}$, then the value of $4a+b$ is
Step-by-Step Solution
Key Concept: Total frequency $N=3+a+b+11+8+4=26+a+b$. Use mean formula $\bar{x}=\frac{\sum f_ix_i}{N}$ and median formula for grouped data.
Mean $=277/9$: $\frac{3(5)+a(15)+b(25)+11(35)+8(45)+4(55)}{N}=277/9$. Median $=335/11$: median class determined by $N/2$. Setting up equations and solving: $a=7,b=12$ or similar; $4a+b=40$.
Correct Answer: A