For a normal distribution, standard empirical relationships link Quartile Deviation (QD), Mean Deviation (MD), and Standard Deviation (SD / $\sigma$):

• $\text{Mean Deviation} = \sqrt{\frac{2}{\pi}}\sigma \approx 0.7979\sigma \approx \frac{4}{5}\sigma \implies 5 \times \text{MD} = 4 \times \text{SD}$ (Option 1 is correct).
• $\text{Quartile Deviation} = 0.6745\sigma \approx \frac{2}{3}\sigma \implies 3 \times \text{QD} = 2 \times \text{SD}$ (Option 2 is correct).
  The overall ratio of dispersion measures is: $$\text{QD} : \text{MD} : \text{SD} = \frac{2}{3}\sigma : \frac{4}{5}\sigma : \sigma = 10 : 12 : 15$$
  Because both Option 1 and Option 2 are mathematically and practically valid for a normal distribution, NTA's official final answer key correctly recognized both '1' and '2' as valid answers.

Calculations:

• Total sum of all 21 numbers $= 21 \times 9 = 189$.
• If the number 19 is removed, the sum of the remaining 20 numbers is:
  $$\text{New Sum} = 189 - 19 = 170$$
• The mean of the remaining 20 numbers is:
  $$\text{New Mean} = \frac{170}{20} = 8.5$$

The median is a positional measure of central tendency. For $N = 100$ observations arranged in ascending order, the median depends solely on the 50th and 51st observations:

Increasing the largest 10 observations (the 91st through 100th values) does not alter the values or positions of the middle 50th and 51st observations. Consequently, the median remains 36.9 unchanged.
Extreme value insensitivity is one of the chief robust properties of the median.