## 1/27/2023

## Problem Session - Gummi bear experiments and class exercises

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

- Measuring Center
- 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.

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