📊 Data and Statistics Reference
🎯 Key Concepts
Data Set
A collection of numbers or values that we want to analyze.
Measures of Center
Numbers that describe where the “middle” of the data is located.
Measures of Spread
Numbers that describe how spread out the data is.
Probability
The likelihood that an event will occur, expressed as a number between 0 and 1.
📐 Measures of Center
Mean (Average)
$$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$$
Usage: Find the average of a set of numbers Example: Mean of 2, 4, 6, 8 is $\frac{2+4+6+8}{4} = 5$
Median
The middle value when data is arranged in order.
Usage: Find the middle value of a data set Example: Median of 1, 3, 7, 9, 12 is 7 (middle value)
Mode
The value that appears most frequently in the data set.
Usage: Find the most common value Example: Mode of 2, 3, 3, 4, 5 is 3 (appears twice)
📏 Measures of Spread
Range
$$\text{Range} = \text{Maximum value} - \text{Minimum value}$$
Usage: Find how spread out the data is Example: Range of 2, 5, 8, 12 is $12 - 2 = 10$
Standard Deviation
$$\sigma = \sqrt{\frac{\sum(x_i - \mu)^2}{n}}$$
Usage: Measure how spread out data is from the mean Note: Usually calculated with calculator for MATHCOUNTS
🎲 Probability Basics
Basic Probability
$$P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$
Usage: Find probability of a simple event Example: Probability of rolling a 3 on a die is $\frac{1}{6}$
Complementary Events
$$P(\text{not A}) = 1 - P(\text{A})$$
Usage: Find probability of the opposite event Example: If $P(\text{rain}) = 0.3$, then $P(\text{no rain}) = 1 - 0.3 = 0.7$
📊 Data Representations
Frequency Table
Shows how often each value appears in the data.
Histogram
A bar graph showing the distribution of data.
Box Plot
Shows median, quartiles, and outliers in the data.
Scatter Plot
Shows relationship between two variables.
💡 Problem-Solving Strategies
- Identify what you’re looking for (mean, median, mode, etc.)
- Organize the data in order if needed
- Use the appropriate formula or method
- Check your answer with estimation
- Consider outliers and their effects
⚠️ Common Mistakes
- Confusing mean and median in calculations
- Forgetting to order data before finding median
- Miscounting outcomes in probability
- Missing the complement in probability problems
- Wrong units in calculations