Statistics Chapter 1.3 and 1.4 Quiz

Announcements

• Quiz 1 grades posted on Gradescope
• Quiz 1 answers in "Quiz Answer Keys" folder
• Homework 2 due Friday 11:59 pm, extended to Sunday 11:59 pm
• Download Excel file (will be done after class)
• No quiz this week

Chapter 1.3 and 1.4

• Chapter 2.1 focuses on examining numerical data

Mean

• Sample mean (X) calculated as the sum of all data points ( Σxi) divided by the total number of data points (n)
• Population mean is calculated the same way, but denoted differently.
• Sample mean is a point estimate of the population mean
• Estimation may not be perfect, but is usually a good estimate if the sample is representative of the population

Histograms

• Histograms show data density
• Convenient for describing modality, shape (skewness), and outliers of the data
• Bin width choice affects the histogram's interpretation

Bin Width

• Some histograms are too detailed (show too much detail), some hide data too much. Analyzing histogram bin-width is important for good data visualization.

Shape of a Distribution: Modality

• Inspect the histogram for a single peak (unimodal), multiple peaks (bimodal/multimodal), or no distinct peak (uniform).

Shape of a Distribution: Skewness

• Determine if a histogram is right-skewed, left-skewed, or symmetric
• Skewness is determined by the position of the tail (longer tail).

Shape of a Distribution: Unusual Observations

• Identify unusual data points or outliers in a histogram, far away from majority of the data values.

Commonly Observed Shapes of Distributions

• Visual representation of common distribution shapes

Variance

• Variance (s²) measures the average squared deviation from the mean
• Standard deviation (s) is the square root of the variance
• It's useful to see how far data is spread out from the mean

Deviation

• Deviation = Distance of an observation from the mean

Median

• The median is the middle value when data is sorted in ascending order
• If an even number of values, median found by averaging the middle two values.

Q1, Q3, and IQR

• Q1 (25th percentile) = first quartile
• Q2 (50th percentile) = median
• Q3 (75th percentile) = third quartile
• IQR = Q3 - Q1 (middle 50% range)

Box Plot

• Box plot displays data distribution through a box (IQR) and whiskers
• Shows outliers outside the whiskers

Whiskers and Outliers

• Whiskers extend up to Q3 + 1.5 * IQR and down to Q1 - 1.5 * IQR
• Outliers are data points beyond the max or min whiskers boundaries

Outliers (continued)

• Outliers may represent data collection errors or unusual data patterns
• Identify outliers to potentially find errors in data or unusual characteristics.

Robust Statistics

• Robust statistics is not greatly affected by extreme data values (outliers)

Mean vs. Median

• If data is symmetric, the mean can be used to represent the center
• In skewed distributions or with extreme outliers, the median represents the center better.

Practice

• Determine if the distribution of note-taking time vs. social media usage is likely left-skewed

Categorical Data

• Involves analysis using numerical values, like counts.

Contingency Tables

• A table visualizing the distribution of categorical data by groups or categories.

Bar Plots

• Display frequency or percentages of categorical data
• Unlike histograms, they don't use bins for continuous data visualization.

Choosing the Appropriate Proportion

• Analyze relationships between categorical variables (e.g., gender and looking for spouse).