Activity 13

MATH 216: Statistical Thinking

Activity 1: EPA gas mileage

  1. Calculate the IQR and standard deviation.

  2. Compute the IQR to standard deviation ratio.

  3. Discuss whether the data appear to be normally distributed based on the ratio calculations and visuals.

Data Transformations and Normality Assessment

Time Allocation: 15 minutes total (5 min reading, 10 min individual work)

Part 1: Understanding Data Distributions (3 minutes)

Instructions: Answer the following conceptual questions:

  1. Why might real-world data often not follow perfect normal distributions?
  1. What are common data transformations used to achieve normality, and when is each appropriate?
  1. How can the IQR-to-standard-deviation ratio help assess normality?

Part 2: EPA Gas Mileage Analysis (4 minutes)

Dataset: Simulated EPA gas mileage data for 100 vehicles (mpg values)

Calculate:

  • Mean mpg =
  • Standard deviation =
  • Q1 (25th percentile) =
  • Q3 (75th percentile) =
  • IQR = Q3 - Q1 =
  • IQR/\(\sigma\) ratio =

Normality Assessment: Based on the IQR/SD ratio, does this data appear normally distributed? Why or why not?

Part 3: Transformation Analysis (3 minutes)

Compare the original and transformed data:

Transformation Purpose When to Use
None (original) Baseline -
Logarithmic
Square Root

Critical Thinking: Why might transforming data be controversial in some statistical analyses?