Study Guide: Key Topics for Statistics Exam (MTH 155)

Topics to Study for Statistics Exam

This guide outlines the essential topics and concepts you should review for your upcoming statistics exam. Each topic is foundational for understanding introductory statistics at the college level.

1. Sample/Population

• Sample: A subset of individuals or items selected from a larger group (population).

• Population: The entire group of individuals or items of interest in a study.

• Example: Surveying 100 students (sample) from a university of 10,000 students (population).

2. Statistic/Parameter

• Statistic: A numerical value calculated from a sample (e.g., sample mean $\bar{x}$).

• Parameter: A numerical value that describes a characteristic of a population (e.g., population mean $\mu$).

• Example: The average height of sampled students (statistic) vs. the average height of all students (parameter).

3. Descriptive/Inferential Statistics

• Descriptive Statistics: Methods for summarizing and organizing data (e.g., mean, median, mode, graphs).

• Inferential Statistics: Methods for making predictions or inferences about a population based on sample data.

• Example: Calculating the mean test score (descriptive) and using it to estimate the population mean (inferential).

4. Levels of Measurement

• Nominal: Categories with no natural order (e.g., gender, colors).

• Ordinal: Categories with a meaningful order but no consistent difference between values (e.g., rankings).

• Interval: Ordered categories with equal intervals but no true zero (e.g., temperature in Celsius).

• Ratio: Ordered categories with equal intervals and a true zero (e.g., height, weight).

5. Sampling Methods

• Random Sampling: Every member of the population has an equal chance of being selected.

• Systematic Sampling: Selecting every k-th member from a list.

• Convenience Sampling: Selecting individuals who are easiest to reach.

• Stratified Sampling: Dividing the population into subgroups and sampling from each subgroup.

• Cluster Sampling: Dividing the population into clusters, then randomly selecting clusters and sampling all members within them.

6. Observational Study/Experiment

• Observational Study: Observing subjects without manipulating variables.

• Experiment: Manipulating one or more variables to observe the effect on another variable.

• Example: Observing students' study habits (observational) vs. assigning different study methods (experiment).

7. Common Data Displays

• Bar Graph: Used for categorical data.

• Pareto Chart: Bar graph with bars ordered by frequency.

• Pie Chart: Shows proportions of categories as slices of a circle.

• Histogram: Used for quantitative data, showing frequency of data intervals.

• Stem-and-Leaf Plot: Displays quantitative data to show distribution.

• Time-Series Graph: Plots data points in time order.

8. Graph Misrepresentation

• Be aware of misleading graphs (e.g., inappropriate scales, omitted baselines, distorted proportions).

• Example: A bar graph with a truncated y-axis exaggerates differences.

9. Frequency Distributions

• Frequency Distribution: A table that displays the frequency of various outcomes in a sample.

• Relative Frequency: The proportion of observations within a category.

• Cumulative Frequency: The sum of frequencies for all categories up to a certain point.

10. Identifying Distributions

• Recognize and describe distributions as normal, skewed, or uniform.

• Normal Distribution: Symmetrical, bell-shaped curve.

• Skewed Distribution: Data is stretched more to one side (left or right).

11. Calculating Percent Change

• Percent Change Formula:

$\text{Percent Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\%$

• Distinguish between "percent of" (a portion of a whole) and "percent change" (increase or decrease relative to the original value).

12. Using a Calculator

• Be familiar with calculator functions for statistics (mean, standard deviation, etc.).

13. Find and Interpret Index Numbers

• Index Number: A measure that reflects changes in a variable or group of variables over time, often expressed relative to a base value of 100.

• Example: Consumer Price Index (CPI) tracks changes in the cost of living.

Exam Instructions and Policies

• Follow all instructions regarding exam setup, calculator use, and academic integrity.

• Do not use unauthorized resources or communicate with others during the exam.

• Show your photo ID as required.

• Violations may result in a grade reduction or a zero.