Data Management and Presentation

• These study notes cover data management, data presentation, graphs, measures of central tendency and dispersion, probability, and correlation

Module 6: Data Management and Presentation

• Data consists of facts that provide information, offering a partial view of a situation
• Ethical data handling is crucial for respecting rights, maintaining trust, and upholding moral principles
• Principles include keeping information safe, honesty, clarity, and obtaining agreement

Data Presentation Methods

• Textual presentation: Combines text and numerical data in reports using sentences, paragraphs, or entire documents to communicate ideas and information
• Tabular presentation: Organizes data in rows and columns for numeric values and independent data
• A table is a data set arranged in rows and columns

Graphical Presentation

• Graphs are visual tools displaying data at a glance to facilitate comparison and reveal trends/relationships
• Forms include charts, graphs, and pictures

Data Types

• Categorical data: Organizes items into groups based on characteristics like gender, eye color, or course
• Numerical data: Uses exact numerical values, examples include height, weight, age, pulse rate, or number of children
• Discrete variables: Numerical data obtained by counting
• Continuous variables: Numerical data obtained by measuring

Data Definitions

• Data: A set of raw facts, that gives a partial picture of reality
• Information: Processed, organized data providing context

Module 7: Interpreting Graphs

• Graphs are visual tools mapping data with dots and lines depicting connections
• Graphical Types
• Bar graph: Uses rectangular bars to represent and easily compare data
• Line graph: Illustrates changes over time, useful for spotting patterns and trends
• Histogram: Displays the distribution of continuous data
• Pie chart: A circular graph divided into slices showing how different parts make up a whole
• Scatter plot: Explores relationships between two variables using plotted points

Ethical Graph Analysis

• Data integrity: Ensuring data accuracy and reliability
• Transparency: Presenting information clearly and understandably with labeled axes and context
• Fair representation: Graphs should not hide information and should depict the complete picture

Module 8: Measures of Central Tendency

• Central tendency measures identify the "middle" or "center" of a dataset
• Mean represents the average, calculated by summing all numbers and dividing by the count of numbers
• Median represents the middle value when data is arranged in order
• Mode represents the most frequently occurring number

Understanding Data Types

• Nominal data: Categories without a specific order
• Ordinal data: Categories with a specific order

Solving Central Tendency Problems

• Calculate the weighted mean by accounting for the varying importance (weights) of each number
• Example: Calculating the average movie rating considering varied follower counts for each reviewer

Module 9: Measures of Dispersion

• Measures of dispersion quantify the spread or variability within a dataset
• Range: Calculated as the difference between the highest and lowest values, expressed as R = HV - LV
• Variance: Measures the average of squared differences from the mean
• Standard Deviation: Measures the average distance of data points from the mean
• Interquartile Range (IQR): Used when there are outliers in the dataset

Identifying Data Measures

• Essential steps to finding the most appropriate measure of dispersion
• Understand the data
• Consider the measurement scale,
• Assess data distribution, and determine the presence of potential outliers

Problem Example

• To find the average number of study hours per week of 10 students
• Compute the mean of the data
• Find each data point’s difference from the mean value
• Square each of these values
• Add up all the squared values
• Divide this sum of squares by n-1
• Take the square root of the variance to get the standard deviation

Module 10: Tree Diagrams & Basic Probability

• Tree diagrams visually represent possible outcomes of events or decisions
• Key rules for probabilities calculations include addition and multiplication rules
• Addition rule which is used when events are connected
• Multiplication rule, used when events are independent

Basic Probability Computations

• Calculating probability for equally likely outcomes as P(A) = Number of favorable outcomes / Total number of possible outcomes

Tree Diagram Steps

• Key steps to using tree diagrams
• Identify the events, list all outcomes for each event, and draw the tree diagram
• Determine probabilities and calculate combined probabilities for each path
• List all possible outcome probabilities

Module 11: Probabilities of Normal Distribution

• Normal Distribution is a symmetric probability distribution where values cluster around the mean, forming a bell curve

Standard Normal Distribution Characteristics

• Mean = 0 and standard deviation = 1. It Allows for standardizing values across distributions
• All normal distributions are symmetric with a bell-shaped density curve and single summit
• Curve asymptotes approach the x-axis
• The standard normal distribution has a mean of 0 and standard deviation of 1

Normal Distribution

• A normal distribution can be standardized to compare values from different distributions using the z-score formula:

Standard Score (z-score)

• Helps determine how far a sample value is from the average in terms of standard devations
• Cases:
• P(z < a): The likelihood is to have a z-score less than a
• P(z > a): The likelihood is to have a z-score greater than a
• P(a < z < b): The likelihood is to have a z-score that falls between those two values

Module 12: Pearson-r Correlation Coefficient & Regression Line

• Linear Relationship is described by an ongoing change, that forms into a straight line on a graph as one changes
• We use linear correlation to describes as one closely follows the straight-line relationship
• Pearson coefficient r measures the stregth of the realtionship for two varibles
• Essential for assessing whether a linear connection among two variables exist

Pearson Product Moment Coefficient of Correlation

• Pearson Formula
• We have X as the observed data for the independent variable
• We have Y as the observed data for the dependent variable
• ∑xy is the sum of the product of x and y
• ∑x ∑y, the product of x and y
• ∑x2, is the sum of the square x
• ∑y2, is the sum of the square y and n equals the paired observations

Correlation Values

• Understanding the value of r uses correlation
• If r = +1, then it is recognized as a posotive relationship whereas -1 is negative
• r = +0, then the relation shop is neutral

Equation

• We can get ŷ, what is predicted ( 𝑦=𝑎+𝑏𝑥 )
• Solving A and B
• Solving for a, 𝑎= ∑𝑦−𝑏∑𝑥/𝑛