MATH 1010 Exam 3 Review Problems

Exam 3 Cheat Sheet

Section 5A: Population and Sample

Population: Entire group of interest.

Sample: Subset of the population.

Sample Statistic: Summarizes sample data.

Population Parameter: Summarizes population data.

Types of Sampling

Simple Random: Equal chance of selection.

Stratified: Random sample from subgroups.

Systematic: Every kth member.

Convenience: Easily available individuals.

Types of Studies

Experiment (single/double blinding): Control for bias.

Observational Study: Observe without manipulation.

Case-Control Study: Compare groups with/without condition.

Representative Sample

Accurately reflects population characteristics.

Margin of Error

Range likely to contain population parameter.

Section 6A: Descriptive Statistics

Outliers: Extreme values affecting the mean.

Skewness: Asymmetry of distribution.

Left-skewed: Skewed to the left.

Right-skewed: Skewed to the right.

Symmetric: Evenly distributed.

Distribution Shapes

Normal: Bell-shaped, symmetric.

Multimodal: Multiple peaks.

Section 7A: Probability

Subjective Method: Based on personal belief.

Probabilities range from 0 to 1.

Probability of 1: Certain event.

Probability of 0: Impossible event.

Confidence Interval

Range where a parameter likely falls.

Measures of Central Tendency

Mean: Average value.

Median: Middle value.

Mode: Most frequent value.

Measures of Variation

Range: Max - Min value.

Five-Number Summary

Min, Q1, Median, Q3, Max.

Boxplots

Visual representation of five-number summary.

Standard Deviation

$s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$

Range Rule of Thumb

$s \approx \frac{Range}{4}$

Empirical Rule (68-95-99.7 Rule)

68% within 1 standard deviation.

95% within 2 standard deviations.

99.7% within 3 standard deviations.

Z-Score

$z = \frac{x - \mu}{\sigma}$

Combinations

Multiply possibilities.

Permutations

Arrangements matter.

Probability Calculations

$P(event) = \frac{Favorable \; Outcomes}{Total \; Outcomes}$

Relative Frequency Method

$P(event) = \frac{Number \; of \; times \; event \; occurred}{Total \; number \; of \; observations}$

Odds

$$Odds = \frac{P(