From study guide posted

Question 1

What is data?

Answer 1

Raw facts or figures

Question 2

What is statistics and what does it involve?

Answer 2

The study of data, involving:
Collecting data
Summarizing data
Drawing conclusions

Question 3

Descriptive vs inferential statistics

Answer 3

Descriptive: Summarizes data.

Inferential: Makes predictions or inferences about a population from a sample.

Question 4

What is population data?

Answer 4

Often not feasible to obtain due to size or time constraints.

Question 5

Cross-sectional vs time series data

Answer 5

Cross-sectional: Data collected at one point in time.

Time series: Data collected over multiple time periods.

Question 6

Structured vs unstructured data

Answer 6

Structured: Organized (e.g., in tables).

Unstructured: Disorganized (e.g., text, images).

Question 7

What is a variable?

Answer 7

A characteristic that can take different values.

Question 8

Categorical vs numerical data

Answer 8

Categorical: Qualitative (e.g., gender, type).

Numerical: Quantitative (e.g., height, age).

Question 9

Discrete vs continuous data

Answer 9

Discrete: Countable (e.g., number of cars).

Continuous: Measurable (e.g., weight, height).

Question 10

What are the four scales of measurement?

Answer 10

Nominal: Categories (e.g., gender).

Ordinal: Ordered categories (e.g., rankings).

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

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

Question 11

How do you deal with missing data?

Answer 11

Omission: Remove missing values.

Imputation: Fill in missing values with estimates.

Question 12

What is frequency distribution?

Answer 12

Summarizes data into categories or intervals.

Question 13

How do you visualize categorical data?

Answer 13

Bar chart
Pie chart
Contingency table
Stacked column chart

Question 14

How do you visualize numeric data?

Answer 14

Histogram: For continuous data.

Intervals: Calculate width by (Max - Min) / Number of intervals.

Skewness: Symmetric, Positive, or Negative.

Question 15

What are three ways to measure central location?

Answer 15

Mean, median, and mode.

Mean (μ for population, x̄ for sample)

Median (especially useful for outliers)

Mode (Unimodal, Bimodal)

Question 16

What is a box plot?

Answer 16

Graphical representation of the five-number summary.

Question 17

What is the five-number summary?

Answer 17

Min, Q1, Median (Q2), Q3, Max.

Question 18

What are the measures of dispersion?

Answer 18

Range: Max - Min.

Interquartile Range (IQR): Q3 - Q1.

Variance (s² for sample, σ² for population) and Standard Deviation (s for sample, σ for population).

Coefficient of Variation (CV): s/x̄ or σ/μ.

Question 19

What is the empirical rule?

Answer 19

For normal distribution, 68%-95%-99.7%.

Question 20

What is a sample space?

Answer 20

Set of all possible outcomes.

Example: S = {A, B, C, D, F} (letter grades).

Question 21

Exhaustive vs mutually exclusive events

Answer 21

Exhaustive: Covers all outcomes.

Mutually Exclusive: Cannot occur simultaneously.

Question 22

Compare union, intersection, and complement

Answer 22

Union (A ∪ B): Outcomes in A or B (or both).

Intersection (A ∩ B): Outcomes in A and B.

Complement (Aᶜ): Outcomes not in A.

Question 23

What are the properties of probability?

Answer 23

0 ≤ P(A) ≤ 1.
Sum of probabilities of mutually exclusive events equals 1.

Question 24

Types of counting

Answer 24

Factorials: For multistep experiments.

Combinations: Selection without order (n choose x).

Permutations: Selection with order.

Question 25

Binomial distribution

Answer 25

Success or failure, fixed trials.

Question 26

Poisson Distribution

Answer 26

Number of successes in a fixed time or space.

Question 27

Normal Distribution

Answer 27

Bell-shaped curve, use cumulative distribution for probabilities.

Question 28

Exponential Distribution

Answer 28

Time/space between events.

Question 29

Expected Value

Answer 29

E(X) = μ = Σ(xᵢ * P(X = xᵢ)).

Question 30

Variance and Standard Deviation

Answer 30

Variance = Σ(xᵢ - μ)² * P(X = xᵢ), SD = √Variance.

Question 31

Confidence interval formula

Answer 31

CI = x̄ ± Z (σ/√n).