Step 2:
Variance $\sigma^2=\large\frac{\sum f_i x_i^2}{\sum f_i} - \bigg(\large\frac{\sum f_ix_i }{\sum f_i } \bigg)^2$
$160 =\large\frac{92 A^2}{7} -\bigg( \large\frac{22A}{7}\bigg)^2$
$160 = \large\frac{92 A^2}{7} -\large\frac{484 A^2}{49}$
$160= \large\frac{92 \times 7A^2 -484A^2}{49}$
$160 \times 49 =644 A^2 -484 A^2$
$160 \times 49= 160 A^2$
$A^2= \large\frac{160 \times 49}{160}$
$A^2= 49$
$A=\pm 7$
Given A is a positive integer .
The value of A is 7.
Hence C is the correct answer.