1/27/2023

Problem Session - Gummi bear experiments and class exercises

Descriptive Statistics (with data from Data Survey - Open DescriptiveStats.R)

• Measuring Center
  • Mean
  • Median
  • Trimmed Mean
• Measuring Spread or Variability
  • Range
  • Interquartile range
  • Variance
  • Standard Deviation
• Measuring Position
  • Percentiles
  • Five-number Summary
  • Boxplot
  • Standardized Scores
• Identifying Outliers
  • 1.5 x IQR Criterion
  • 2 or 3 standard deviations away from the mean

Standard deviation contest: You must choose 4 numbers from the set {0, 1, 2, ..., 10} with repeats allowed.

• Choose 4 numbers that have the smallest possible standard deviation.
• Choose 4 numbers that have the largest possible standard deviation.

Empirical Rule

• If the histogram of values in a data set can be reasonably approximated by a Normal curve, then
  • approximately 68% of the observations are within 1 standard deviation of the mean
  • approximately 95% of the observations are within 2 standard deviation of the mean
  • approximately 99.7% of the observations are within 3 standard deviation of the mean

Class Exercises

The responses from our Day 1 Survey (Google Form) can be found in the file Google Drive\Stat106-ElementsofStatistics-S2023\!Class-csv-Rscripts\ClassDataS23_Updated.csv. Use this file for the exercises below.

1. Are the students in Elements of Statistics evenly split with respect to Cats or Dogs?
2. Is the distribution of students evenly spread across all four years of current students?
3. Do you think there is a relationship between Section and Handedness? Explain.
4. Do you think there is a relationship between Section and Cats or Dogs? Explain.

We will have our first quiz next Friday. Please read Section 2.3 for class on Monday.