Statistics
Variance of Frequency Distribution — Finding c
nta_pyq_2024_apr
Grade 11
Question:
If the variance of the frequency distribution
| $x$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ |
|---|---|---|---|---|---|---|
| $f$ | 2 | 1 | 1 | 1 | 1 | 1 |
is 160, then the value of $c\in\mathbb{N}$ is
Step-by-Step Solution
Key Concept: Total frequency $N=7$. $\bar{x}=\frac{(2+2+3+4+5+6)c}{7}=\frac{22c}{7}$. $\text{Var}=\frac{c^2(2\cdot1^2+2^2+3^2+4^2+5^2+6^2)}{7}-\left(\frac{22c}{7}\right)^2=\frac{92c^2}{7}-\frac{484c^2}{49}$.
$c^2=49$, so $c=7$.
Correct Answer: 1