Let the original prices of the 5 tables be $\(P=\{190,210,175,230,163\}\)$.
Understanding Standard Deviation (S.D.) and its properties:
- Adding/Subtracting a Constant: If a constant value is added to or subtracted from every number in a dataset, the standard deviation of the dataset does not change. The spread of the data remains the same, only the center shifts.
- Multiplying/Dividing by a Constant: If every number in a dataset is multiplied or divided by a constant value, the standard deviation of the dataset is also multiplied or divided by the absolute value of that same constant. The spread of the data changes proportionally.

Quantity A: S.D. of final prices if a discount of \(\$100\) is given on price of each table

This is equivalent to subtracting a constant value (100) from each original price.
Let the original standard deviation of the prices be $\(S D_{\text {original }}\)$.
The new prices will be $\(\{190-100,210-100,175-100,230-100,163-100\}\)$ $\(=\{90,110,75,130,63\}\)$.

According to the property of standard deviation, subtracting a constant from each data point does not change the standard deviation.
So, Quantity A $\(=S D_{\text {original }}\)$.

Quantity B: S.D. of the final prices if a discount of $10 %$ is given on prices of each table
This is equivalent to multiplying each original price by $\((1-10 %)=0.90\)$.
The new prices will be $\(\{190 \times 0.9,210 \times 0.9,175 \times 0.9,230 \times 0.9,163 \times 0.9\}\)$.
According to the property of standard deviation, multiplying each data point by a constant (0.90) will multiply the standard deviation by that same constant.
So, Quantity B $\(=S D_{\text {original }} \times 0.90\)$.

Comparison:
We need to compare Quantity A ( $\(S D_{\text {original }}\)$ ) with Quantity B ( $\(S D_{\text {original }} \times 0.90\)$ ).
Since the prices are different, $\(S D_{\text {original }}\)$ must be a positive value ( $\(S D_{\text {original }}>0\)$ ).
We are comparing $\(S D_{\text {original }}\)$ with $\(0.90 \times S D_{\text {original }}\)$.
Since $\(0.90<1\)$, it means $\(0.90 \times S D_{\text {original }}\)$ will be smaller than $\(S D_{\text {original }}\)$.
Therefore, Quantity A is greater than Quantity B.
The final answer is Quantity A is greater.