Mean, Median, Mode, and Range
Key Concepts
- Mean (average): \text{sum} \div \text{count}
- Median: middle number when sorted
- Mode: most frequent value
- Range: max – min
Skills Tested
- Calculating measures of central tendency
- Identifying how changes in data affect the mean
- Comparing multiple data sets
Example Question
What is the mean of the numbers: 4, 8, 6, 2, 10? A. 6 B. 5 C. Answer: 6 (Mean = \frac{4+8+6+2+10}{5} = \frac{30}{5} = 6)
Interpreting Data Sets and Graphs
Key Concepts
- Reading bar graphs, line graphs, histograms, boxplots, and scatterplots
- Trends, outliers, and comparisons
Skills Tested
- Extracting info from visual representations
- Understanding shape and spread of data
- Identifying medians, quartiles, and outliers in boxplots
Example Question
A boxplot shows a data set with Q1 = 25, median = 40, Q3 = 60. What is the interquartile range (IQR)? A. 35 B. 20 C. Answer: 35 (IQR = Q3 - Q1 = 60 - 25 = 35)
Probability
Key Concepts
- Basic probability: \frac{\text{favorable}}{\text{total}}
- Compound events: "and" = multiply, "or" = add (for disjoint events)
- Independent vs. dependent events
Skills Tested
- Calculating probabilities of single and multi-step events
- Understanding complementary probability: P(\text{not A}) = 1 - P(A)
- Working with tables or scenarios
Example Question
A bag has 5 red, 3 blue, and 2 green marbles. What is the probability of drawing a blue marble? A. 30% B. Answer: \frac{3}{10} (Total = 10; blue = 3 → \frac{3}{10})
Combinations and Permutations
Key Concepts
- Permutations (order matters): nPr = \frac{n!}{(n - r)!}
- Combinations (order doesn’t matter): nCr = \frac{n!}{r!(n - r)!}
Skills Tested
- Recognizing when order matters
- Applying factorials and formulas
- Solving counting problems efficiently
Example Question
How many ways can 3 students be chosen from a group of 5 to form a committee (order doesn't matter)? A. 60 B. Answer: 10 (Use combinations: \binom{5}{3} = \frac{5!}{3!2!} = 10)
Statistical Modeling and Interpretation
Key Concepts
- Line of best fit in scatterplots
- Identifying positive, negative, or no correlation
- Making predictions from models or equations
Skills Tested
- Recognizing the meaning of slope and intercept
- Interpreting scatterplot trends
- Using models to make extrapolations or interpolations
Example Question
A line of best fit for a data set is y = 2x + 5. What does the slope mean in context? A. For every 1-unit increase in x, y increases by 2 B. Answer: A (Slope represents rate of change)