Core Statistical Concepts: Data, Inference & Models
Understanding Data Types
Different types of data require different analytical approaches:
- Cross-sectional data: Characteristics of many subjects or observations at the same point in time.
- Time series data: Data focusing on one observation over several time periods.
- Cross-sectional time series data: A collection of observations for multiple subjects at multiple time periods.
- Panel or longitudinal data: The same subject measured over various time periods.
Quantitative Data
Quantitative data is numerical.
Probability Questions and Solved Examples
Here is the giant combined cheat sheet with all questions, tables, charts, calculations, and answers included. You can copy this into a document editor and save it as a PDF.
Probability Questions and Answers
Question 1
Statement: Tossing a coin and getting a head, and then rolling a 6-sided die and getting a 5. Are these events dependent?
Answer: False
Explanation: The events are independent because the outcome of the coin toss does not affect the die roll.
Question 2
Which pairs of events are disjoint?
Read MoreStatistics Problems and Solutions
1. Blood Cholesterol Analysis
Blood cholesterol was measured on a random sample of 24 people:
226, 189, 240, 192, 216, 207, 221, 255, 190, 237, 219, 182, 209, 198, 243, 202, 234, 194, 213, 185, 193, 223, 204, 191
i) Stem-and-Leaf Plots
The first 18 observations have been entered in the stem-and-leaf plot on the left. The completed plot is shown on the right.
Left Plot (Original Entries in Bold) | Right Plot (Ordered)
25 | 5 | 25 | 5
24 | 0 3 | 24 | 0 3
23 | 7 4 | 23 | 4 7
22 | 6 1 3 | 22 | 1 3 6
21 | 6 9
Read MoreResearch Methods: A Comprehensive Study
Side 1: Chapter 4 – Research Design
Definition
The plan or blueprint for a study, outlining how data will be collected and analyzed.
Types
- Exploratory
- Descriptive
- Causal
Key Research Design Types
Exploratory Research
Conducted when little is known, aims to gain insights and clarify ideas.
Descriptive Research
Provides a detailed description of phenomena, without manipulation.
Causal Research
Establishes cause-and-effect relationships between variables.
Sampling Design
Probability Sampling
Every member of the population
Read MoreKey Concepts in Statistics: Data, Methods & Limitations
Limitations of Statistics
-
Statistics does not deal with individuals:
- Statistics deals with an aggregate of facts and does not give specific recognition to individual items in a series.
- It deals with groups of individuals and indicates the characteristics of the whole group.
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Statistics does not deal directly with qualitative characteristics:
- Statistical methods can only be applied to numerically expressed data.
- A qualitative phenomenon must be converted into quantitative information before statistical
Understanding Statistical Variability and Distributions
Understanding Measures of Variability
Measures of variability indicate how much scores in a distribution vary, either from the mean or across the full extent of the distribution. It represents the spread of all the scores. Four measures of variability are discussed here: the range, the average mean deviation, the variance, and the standard deviation. These measures can reveal the consistency or similarity of the scores in a distribution and the extent to which the mean truly represents all of the
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