10.1.2: Quantitative Variable Analysis
- Page ID
- 63624
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Semester Project: Analyzing a Quantitative Variable (Rental Prices)
In this project assignment, you will perform a thorough analysis the quantitative variables you collected in your Sampling and Data Project: the rental prices for 1-bedroom apartments and their square footage.
Using Excel or another tool, you’ll create frequency tables, visual summaries (histogram and boxplot), and calculate relevant descriptive statistics including mean, median, standard deviation, and five number summary. You’ll use these tools to describe the shape, center, and spread of your data, and interpret your findings in plain language.
Objectives
- Construct a frequency table and histogram
- Construct a boxplot and identify potential outliers
- Describe distribution shape (modality, skew), center, and spread
- Calculate and interpret key statistics: mean, median, range, standard deviation, and five number summary
- Use technology to support analysis
Assignment Steps
- Create a frequency table for rental prices using 5 to 10 evenly spaced class intervals.
- Create a histogram from the frequency table in Excel. Your histogram should include:
- A meaningful chart title
- Clearly labeled axes
- Equal-width bins/classes
- Create a boxplot for rental price data to visually assess spread and potential outliers.
- Calculate the following descriptive statistics:
- Mean
- Median
- Standard Deviation
- Range
- Five number summary
- Repeat #1-4 for the square footage variable
- Summarize the distribution of each variable. This should be a paragraph or two for each. Include:
- Shape of the distribution (modal shape, skewness)
- Noted outliers and what they might represent
- Comparison of mean and median
- What the spread tells you about market variability
- Real-World Interpretation: What does this data tell us about 1-bedroom rental prices in Lakewood? Who might use this information and why? Are any listings significantly higher or lower than average, and what might that mean?
- Circle back to the question you wrote in the data collection part of the project: Can you answer any price-related questions you posed earlier using your visuals or stats?
Helpful Tips
- Class intervals in your histogram should be equal-width, non-overlapping, and intuitive (e.g., $100 increments)
- Use labels: Axis titles and legend titles should match your variable name exactly
- The boxplot is great for visualizing skewness and identifying any extreme outliers
- If your mean is much higher than your median, that might signal right skew (a few expensive listings pulling up the average)