Question

for the age group 21-27 years in bpo industry, the first quartile of monthly income is equal to php 16,500 and the third quartile of monthly income for this same age group is php25,000. calculate the quartile coefficient of variation for the distribution of incomes for this age group. 15.25% 22.5% 30.5% 20.5%

Explanation:

Step1: Recall the formula for quartile coefficient of variation

The formula for the quartile coefficient of variation (QCv) is given by:
$$QCv = \frac{Q_3 - Q_1}{Q_3 + Q_1} \times 100\%$$
where \( Q_1 \) is the first quartile and \( Q_3 \) is the third quartile.

Step2: Identify the values of \( Q_1 \) and \( Q_3 \)

Given:
\( Q_1 = 16500 \) (Php)
\( Q_3 = 25000 \) (Php)

Step3: Substitute the values into the formula

First, calculate \( Q_3 - Q_1 \) and \( Q_3 + Q_1 \):
\( Q_3 - Q_1 = 25000 - 16500 = 8500 \)
\( Q_3 + Q_1 = 25000 + 16500 = 41500 \)

Then, substitute these into the QCv formula:
$$QCv = \frac{8500}{41500} \times 100\%$$

Step4: Simplify the fraction and calculate the percentage

Simplify \( \frac{8500}{41500} \approx 0.2048 \) (or \( \frac{17}{83} \approx 0.2048 \))
Multiply by 100%: \( 0.2048 \times 100\% \approx 20.5\% \) (rounded to one decimal place)

Answer:

20.5% (the option with "20.5%")