# Rental Market Data Analysis Given (sample from 3 apartments): | Monthly Rent | Footage | |--------------|---------| | 645 | 500 | | 675 | 648 | | 2400 | 2700 | ## a. Mean and Standard Deviation of Monthly Rent **Sample:** 645, 675, 2400 ### Mean \[ \bar{x} = \frac{645 + 675 + 2400}{3} = \frac{3720}{3} = 1240.00 \] ### Sample Standard Deviation \[ s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2} \] - \( (645 - 1240)^2 = (-595)^2 = 354025 \) - \( (675 - 1240)^2 = (-565)^2 = 319225 \) - \( (2400 - 1240)^2 = (1160)^2 = 1345600 \) Sum: \( 354025 + 319225 + 1345600 = 2018850 \) \[ s = \sqrt{\frac{2018850}{2}} = \sqrt{1009425} \approx 1004.70 \] - **Mean:** $1240.00 - **Standard deviation:** $1004.70 --- ## b. Mean and Standard Deviation of Footage **Sample:** 500, 648, 2700 ### Mean \[ \bar{x} = \frac{500 + 648 + 2700}{3} = \frac{3848}{3} = 1282.67 \] ### Sample Standard Deviation - \( (500 - 1282.67)^2 = (-782.67)^2 \approx 612573.51 \) - \( (648 - 1282.67)^2 = (-634.67)^2 \approx 402803.51 \) - \( (2700 - 1282.67)^2 = (1417.33)^2 \approx 2008855.11 \) Sum: \( 612573.51 + 402803.51 + 2008855.11 = 3024232.13 \) \[ s = \sqrt{\frac{3024232.13}{2}} = \sqrt{1512116.07} \approx 1229.71 \] - **Mean:** 1282.67 sq ft - **Standard deviation:** 1229.71 sq ft --- ## c. Relative Dispersion (Coefficient of Variation) \[ CV = \frac{s}{\bar{x}} \] - **Monthly Rent:** \( CV = \frac{1004.70}{1240.00} \approx 0.81 \) - **Footage:** \( CV = \frac{1229.71}{1282.67} \approx 0.96 \) ### Conclusion - **Footage** exhibits greater relative dispersion. --- **Summary Table** | | Monthly Rent | Footage | |------------|--------------|---------| | Mean | 1240.00 | 1282.67 | | Std Dev | 1004.70 | 1229.71 | | CV | 0.81 | 0.96 | **Footage sample data exhibit greater relative dispersion.**