Question

a real estate branch manager is in charge of selling houses in two subdivisions. the mean selling price of a new house in green park village is php2.5m with a standard deviation of php150,000. in vista verde, the mean price is php3m and the standard deviation is php250,000. what are the coefficients of variations of the selling price of the two subdivisions? green park = 5.5% & vista verde = 4.8% green park = 6% & vista verde = 8.3% green park = 5% & vista verde = 6.2% green park = 7% & vista verde = 9.3%

Explanation:

Step1: Recall the formula for coefficient of variation (CV)

The coefficient of variation is calculated as \( CV = \frac{\text{Standard Deviation (SD)}}{\text{Mean (M)}} \times 100\% \)

Step2: Calculate CV for Green Park Village

Given:

• Mean (\( M_{GP} \)) = Php2.5M = 2,500,000
• Standard Deviation (\( SD_{GP} \)) = Php150,000

Using the formula:
\( CV_{GP} = \frac{SD_{GP}}{M_{GP}} \times 100\% = \frac{150000}{2500000} \times 100\% \)
\( \frac{150000}{2500000} = 0.06 \), so \( CV_{GP} = 0.06 \times 100\% = 6\% \)

Step3: Calculate CV for Vista Verde

Given:

• Mean (\( M_{VV} \)) = Php3M = 3,000,000
• Standard Deviation (\( SD_{VV} \)) = Php250,000

Using the formula:
\( CV_{VV} = \frac{SD_{VV}}{M_{VV}} \times 100\% = \frac{250000}{3000000} \times 100\% \)
\( \frac{250000}{3000000} \approx 0.0833 \), so \( CV_{VV} \approx 0.0833 \times 100\% \approx 8.3\% \)

Answer:

Green Park = 6% & Vista Verde = 8.3% (corresponding to the option "Green Park = 6% & Vista Verde = 8.3%")