📊 Introductory Statistics – Chapter 2:
Central Tendency & Spread
📖 Chapter Overview
This chapter focuses on methods to summarize and describe the center and spread of
data. It introduces measures of central tendency (mean, median, mode) and measures
of variation (range, interquartile range, standard deviation, and variance).
🧾 Cheat Sheet
- Mean: The arithmetic average (sum of values ÷ number of values)
- Median: The middle value when data is sorted
- Mode: The most frequent value
- Range: Max - Min
- Interquartile Range (IQR): Q3 - Q1 (middle 50% of data)
- Variance (σ²): Average of squared deviations from the mean
- Standard Deviation (σ): Square root of the variance
Rules of Thumb:
- Mean is sensitive to outliers
- Median is resistant to outliers
- Use standard deviation when data is symmetric; use IQR when skewed
🧠 Practice Problems
1. Find the mean, median, and mode:
Dataset: 12, 15, 15, 18, 20
Answer:
- Mean = (12+15+15+18+20)/5 = 16
- Median = 15
- Mode = 15
2. Find the range and standard deviation (sample):
Dataset: 10, 12, 14, 16, 18
Central Tendency & Spread
📖 Chapter Overview
This chapter focuses on methods to summarize and describe the center and spread of
data. It introduces measures of central tendency (mean, median, mode) and measures
of variation (range, interquartile range, standard deviation, and variance).
🧾 Cheat Sheet
- Mean: The arithmetic average (sum of values ÷ number of values)
- Median: The middle value when data is sorted
- Mode: The most frequent value
- Range: Max - Min
- Interquartile Range (IQR): Q3 - Q1 (middle 50% of data)
- Variance (σ²): Average of squared deviations from the mean
- Standard Deviation (σ): Square root of the variance
Rules of Thumb:
- Mean is sensitive to outliers
- Median is resistant to outliers
- Use standard deviation when data is symmetric; use IQR when skewed
🧠 Practice Problems
1. Find the mean, median, and mode:
Dataset: 12, 15, 15, 18, 20
Answer:
- Mean = (12+15+15+18+20)/5 = 16
- Median = 15
- Mode = 15
2. Find the range and standard deviation (sample):
Dataset: 10, 12, 14, 16, 18
