📊 Data and Statistics Topics#
🎯 Core Subtopics#
Measures of Center#
- Mean: Average of all values
- Median: Middle value when ordered
- Mode: Most frequent value
- Micro-example: Data set 2, 3, 3, 5, 7 has mean 4, median 3, mode 3
- Trap: Forgetting to order data before finding median
Measures of Spread#
- Range: Maximum - Minimum
- Standard Deviation: Measure of spread from mean
- Micro-example: Data set 1, 3, 5, 7, 9 has range 8, mean 5
- Trap: Confusing range with mean
Weighted Averages#
- Weighted Mean: $\frac{\sum(w_i \cdot x_i)}{\sum w_i}$
- Grade Point Average: Common application
- Micro-example: Test scores 80, 90 with weights 2, 3: $\frac{2 \cdot 80 + 3 \cdot 90}{2 + 3} = \frac{430}{5} = 86$
- Trap: Forgetting to divide by total weight
Probability Basics#
- Simple Probability: Favorable outcomes / Total outcomes
- Complementary Events: $P(\text{not A}) = 1 - P(\text{A})$
- Micro-example: Probability of not rolling a 6 is $1 - \frac{1}{6} = \frac{5}{6}$
- Trap: Confusing favorable and total outcomes
Data Representations#
- Frequency Tables: Count of each value
- Histograms: Bar graph of data distribution
- Box Plots: Shows quartiles and outliers
- Micro-example: Data 1, 1, 2, 3, 3, 3 has frequency table: 1 appears 2 times, 2 appears 1 time, 3 appears 3 times
- Trap: Miscounting frequencies
Outliers and Their Effects#
- Outlier: Value far from other data points
- Effect on Mean: Outliers pull mean toward them
- Effect on Median: Median is less affected by outliers
- Micro-example: Data 1, 2, 3, 4, 100 has mean 22, median 3
- Trap: Not recognizing outliers
🚨 Common Traps#
- Median Ordering: Forgetting to order data before finding median
- Weighted Average: Not dividing by total weight
- Probability Counting: Miscounting favorable outcomes
- Outlier Effects: Not considering how outliers affect measures
- Unit Confusion: Mixing different units in calculations
💡 Quick Tips#
- Median: Always order data first
- Mean: Sum all values, then divide by count
- Mode: Find the most frequent value
- Probability: Count carefully, check your work
- Outliers: Consider their effect on your answer