Question

consider the computed quartiles for the given data of the ages of the covid - 19 infected patients in hospitals a and b as shown in the table below. determine the coefficient of quartile deviations of the patients ages at the two hospitals.

	$q_1$ or $p_{25}$	$q_3$ or $p_{75}$	$cdq$
hospital b	46.4	65.6	?

options:

• hospital a = 9.1% & hospital b = 18.34%
• hospital a = 6.97% & hospital b = 17.14%
• hospital a = 8.25% & hospital b = 19.32%
• hospital a = 7.30% & hospital b = 21.4%

Explanation:

The formula for the coefficient of quartile deviation (CDQ) is:
$$CDQ = \frac{Q_3 - Q_1}{Q_3 + Q_1} \times 100$$

Step 1: Calculate CDQ for Hospital A

Given \( Q_1 = 58.7 \) and \( Q_3 = 67.5 \).
Substitute into the formula:
$$CDQ = \frac{67.5 - 58.7}{67.5 + 58.7} \times 100 = \frac{8.8}{126.2} \times 100 \approx 6.97\%$$

Step 2: Calculate CDQ for Hospital B

Given \( Q_1 = 46.4 \) and \( Q_3 = 65.6 \).
Substitute into the formula:
$$CDQ = \frac{65.6 - 46.4}{65.6 + 46.4} \times 100 = \frac{19.2}{112} \times 100 \approx 17.14\%$$

Answer:

Hospital A = 6.97% & Hospital B = 17.14%