VIPSolutionsGive step-by-step solution with explanation and final answer:rr io ul RTL A ealextati adh examines he v OBI i ri t examines the r ina. © town. She. data on monthly rent and the footage for 40 (75 CO CB Cock hare for the Excel Data a Calculate the mean an the standard destaon of monthly nt. (Round your answers 2 decimal places) (IIS ca— 3 [Sundard devon [1] b. Calculate the mean and the standard deviation for footage. (Round your answers to 2 decimal places) ! | —— g h 0 in hi i c. Which sample data exhibit greater relative dispersion? - Lo
Question:
Give step-by-step solution with explanation and final answer:
rr io ul RTL
A ealextati adh examines he v OBI i
ri t examines the r ina. © town. She. data on monthly rent and the footage for 40
(75 CO
CB Cock hare for the Excel Data
a Calculate the mean an the standard destaon of monthly nt. (Round your answers 2 decimal places)
(IIS ca— 3
[Sundard devon [1]
b. Calculate the mean and the standard deviation for footage. (Round your answers to 2 decimal places)
!
| —— g h 0
in hi
i
c. Which sample data exhibit greater relative dispersion? -
Lo
This is AI generated Response.
Asked by: mayank
Created at: 2025-09-19 17:49:52
Asked by: mayank
Created at: 2025-09-19 17:49:52
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Let's solve step-by-step.
## Given Data
| Monthly Rent | Footage |
|--------------|---------|
| 645 | 508 |
| 675 | 648 |
| 2400 | 2780 |
---
## a. Calculate the mean and standard deviation for **monthly rent**
### Step 1: Mean
\[
\text{Mean} = \frac{645 + 675 + 2400}{3}
= \frac{3720}{3}
= 1240.00
\]
### Step 2: Standard Deviation
\[
s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}
\]
Where \( \bar{x} = 1240 \)
- For 645: \( (645 - 1240)^2 = (-595)^2 = 354025 \)
- For 675: \( (675 - 1240)^2 = (-565)^2 = 319225 \)
- For 2400: \( (2400 - 1240)^2 = (1160)^2 = 1345600 \)
Sum: \( 354025 + 319225 + 1345600 = 2028850 \)
Variance: \( \frac{2028850}{2} = 1014425 \)
Standard deviation:
\[
s = \sqrt{1014425} \approx 1007.19
\]
---
### **Answers for (a):**
- **Mean:** 1240.00
- **Standard deviation:** 1007.19
---
## b. Calculate the mean and standard deviation for **footage**
### Step 1: Mean
\[
\text{Mean} = \frac{508 + 648 + 2780}{3}
= \frac{3936}{3}
= 1312.00
\]
### Step 2: Standard Deviation
Where \( \bar{x} = 1312 \)
- For 508: \( (508 - 1312)^2 = (-804)^2 = 646416 \)
- For 648: \( (648 - 1312)^2 = (-664)^2 = 440896 \)
- For 2780: \( (2780 - 1312)^2 = (1468)^2 = 2154624 \)
Sum: \( 646416 + 440896 + 2154624 = 3241936 \)
Variance: \( \frac{3241936}{2} = 1620968 \)
Standard deviation:
\[
s = \sqrt{1620968} \approx 1273.20
\]
---
### **Answers for (b):**
- **Mean:** 1312.00
- **Standard deviation:** 1273.20
---
## c. Which sample data exhibit greater relative dispersion?
**Relative dispersion** is measured by the coefficient of variation (CV):
\[
CV = \frac{s}{\bar{x}}
\]
- **Monthly Rent:** \( CV = \frac{1007.19}{1240.00} \approx 0.813 \)
- **Footage:** \( CV = \frac{1273.20}{1312.00} \approx 0.970 \)
**Footage** has a higher coefficient of variation.
---
### **Final Answers**
#### a. Monthly rent:
- Mean: **1240.00**
- Standard deviation: **1007.19**
#### b. Footage:
- Mean: **1312.00**
- Standard deviation: **1273.20**
#### c. Which sample data exhibit greater relative dispersion?
- **Footage** (because it has a higher CV)
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