Metro Metrics Slides Metro Metrics
Advanced Data Analysis for Urban Engineering
Department of
Urban Analytics
Project Overview
Technical Goals
Engineers utilize data visualization to optimize urban infrastructure. Our objective is to analyze "Metro City" datasets and make precise projections.
Evaluate proportional relationships \(y = kx\)
Analyze population variability via box plots
Resource optimization via circle graphs
Resource Allocation
Parts of a Whole
Metro City's Energy Budget is capped at $4.5 Million.
Solar Power 40%
Wind Power 35%
Hydro-Electric 15%
Other Sources 10%
Analysis Question
Calculate the exact budget difference (in dollars) between Solar and Hydro funding.
Traffic Analysis
Population Comparison
Commute Times (Minutes): East District vs. West District
East District
West District
10
20
30
40
50
60
Median Comparison
The West District has a significantly higher typical commute time (\(50\) min) than the East District (\(30\) min).
Variability Analysis
The East District 's lower IQR (\(20\) min) suggests more consistent and predictable morning traffic.
Cost Projections
Unit Rates
Total Cost in $ (y)
Usage Units (x)
(50, 20)
Calculating \(k\)
The constant of proportionality (\(k\)) identifies the unit rate . For any technical point \((x, y)\):
\[ k = \frac{y}{x} = \frac{20}{50} \]
\(k = \$0.40\) Per Unit
Technical Projection
2,000 units = \$800.00
Data Strategy
STEP_01
Verify Scales
Always check axis units. A value of '100' on a graph labeled 'in thousands' means 100,000.
STEP_02
Isolate \(k\)
Find a 'clean' point on a proportional line to find the unit rate. Use \(y/x\) to make accurate projections.
STEP_03
Variability
A smaller box (IQR) in a box plot indicates more consistent and predictable data points.
City Stats Worksheet City Analytics Dept.
City Stats
Infrastructure Analysis Report
Engineer:
Date_ID:
A
Environmental Resource Allocation
The current municipal fund is set at $1,200,000 . Distribution metrics are provided below.
Solar Power (45%)
Public Parks (30%)
Public Transit (15%)
Waste Mgmt (10%)
Technical Task Q1
Calculate the dollar amount difference between 'Parks' and 'Transit' allocations. Show all mathematical work.
Technical Task Q2
If the Transit budget is increased to 30% by reducing the Solar budget, what is the new Solar percentage?
B
Infrastructure Cost Projections
Total Cost in Thousands ($) (y)
Miles of Roadwork (x)
0
2
4
6
8
0
50
100
150
200
(4, 100)
Task Q3
Calculate the constant of proportionality (\(k\)). Explain the technical meaning of this value for the city budget.
Task Q4
Using the calculated unit rate, determine the total projected cost for 15 miles of roadwork.
C
Traffic Density Statistics
Commute distribution comparison: East District vs West District .
East District
West District
1020304050607080
Task Q5
Which district has the higher median commute time? Determine the numerical difference between the two medians.
Task Q6
Compare the variability of these two districts. Which district has more predictable traffic patterns? Justify using the IQR.
Population Dynamics Projection
A random sample of 50 residents revealed that 18 preferred the 'Digital Literacy' program. If the total city population is 15,000, calculate the projected number of residents who would prefer this program.
Final Analysis Q7
Project Lead Guide Project Lead Guide
Metro Metrics Administration
MCAS_7.RP_7.SP
Learning Objectives
Identify constant of proportionality \((k)\) in visualizations.
Compare populations via measures of center (median) and variability (IQR).
Solve multi-step problems from circle graph distribution data.
Standard Codes
7.RP.A.2 7.SP.A.2 7.SP.B.3
Technical Answer Key
Project Alpha: Resources
Q1: \(30\% - 15\% = 15\%\) diff. Calculation: \(0.15 \times 1,200,000 = \$180,000\).
Q2: Transit \(+15\%\). Solar \(-15\%\). Result: \(45\% - 15\% = 30\%\).
Project Beta: Infrastructure
Q3: \(k = 100 \div 4 = 25\). Cost is $25,000 per mile paved.
Q4: \(25 \times 15 = 375\). Total projected construction cost: $375,000 .
Project Gamma: Traffic Analysis
Q5 (Median): West District (60) > East District (30). Numerical difference is 30 minutes .
Q6 (IQR): East District is more predictable. IQR: 25 min (East) vs 30 min (West). Lower IQR indicates higher consistency.
Q7 Analysis Projection:
\( (18 \div 50) \times 15,000 = 5,400 \) residents
Technical Implementation Notes
Common Error Metrics
Neglecting 'Thousands' scaling on Y-axis.
Confusing the median line with mean in skewness.
Calculating \(k\) as \(x \div y\) (incorrect ratio).
Instructional Strategy
Focus on \(y = kx\) as a predictive model. For box plots, emphasize that the middle 50% (IQR) provides a more robust 'predictability' metric than the total range.
