STATISTICS-WEEK-1-Autosaved

Our Lady of Fatima University

  • Course: Statistics and Probability

Introduction to Statistics

  • Definition: Study of collection, analysis, interpretation, presentation, and organization of data.

  • Key Functions:

    • Collect and summarize data.

    • Conduct research and evaluate outcomes.

    • Develop critical thinking and make informed decisions.

  • Applications: Used in various fields to understand why events happen, when they occur, and predict their reoccurrence.

Importance of Statistics

  • Statistics emphasizes the importance of randomness more than pure mathematics (Probability Theory).

  • Focus is on making predictions related to:

    • Consumer behavior

    • Political preferences

    • Statistical analyses of populations, such as voter demographics.

Understanding Probability

  • Definition: Likelihood of an event occurring, with values expressed between 0 and 1.

  • Key Concepts:

    • Probability = (Number of favorable outcomes) / (Total number of outcomes)

    • Can represent the chance of various outcomes in random events.

  • Examples:

    • Probability of rolling a specific number on a die.

    • Probability of rain in weather forecasts.

Probability vs. Statistics

Overview

Aspect

Probability

Statistics

Purpose

Predict likelihood of events

Analyze and interpret data

Starting Point

Known theoretical model

Observed data

Focus

Future outcomes

Past data

Example Question

"What is the chance of drawing a red card?"

"What percentage of cards drawn were red?"

Practical Examples of Probability

Example 1: Rolling a Die

  • Sample Space: S = {1, 2, 3, 4, 5, 6}

  • Finding Probability:

    • Probability of getting a 5: P(5) = 1/6.

Example 2: Drawing Cards

  • Standard Deck of Cards:

    • Probability of picking a black card: P(Black) = 26/52 = 1/2.

Example 3: Rolling a Die for Even Numbers

  • Find Probability:

    • P(Even) = (Number of Even Numbers) / (Total Outcomes) = 3/6 = 1/2.

Example 4: Drawing a Spade

  • Find Probability:

    • P(Spade) = 13/52 = 1/4.

Classification of Questions

  • Determine whether each question pertains to Statistics or Probability:

    • How old are the people living in Macabling, Laguna? (Statistics)

    • How many chances are there to pick a king in a deck of cards? (Probability)

    • Does it rain often in Laguna than in Cavite? (Statistics)

    • How many chances to get "tail" when tossing a coin? (Probability)

Random Variables

Definition

  • A random variable is defined as a function whose value is determined by the outcome of a random experiment.

Examples

  1. Example 1: Rolling a die

    • Sample Space: S = {1, 2, 3, 4, 5, 6}

    • X (even outcomes): X = {2, 4, 6}

    • Y (odd outcomes): Y = {1, 3, 5}

  2. Example 2: Student test scores

    • For a 10-item test: S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

    • Possible scores Z = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Sample Space and Outcomes

Example 3: Tossing Coins

  • When tossing two coins, the sample space: S = {HH, HT, TH, TT}

  • Probability Tree for heads (X):

    • HH: X = 2

    • HT: X = 1

    • TH: X = 1

    • TT: X = 0

Example 4: Outcomes in Tossing Three Coins

  • Sample Space:

    • S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

  • Outcomes where exactly two heads occur: HHT, HTH, THH.

Types of Random Variables

Discrete Variable

  • Definition: Takes on a limited or countable number of values.

  • Examples:

    • Number of boys in a classroom.

    • Number of words in a poetry reading.

Continuous Variable

  • Definition: Can take any value within certain intervals, representing measured data.

  • Examples:

    • Weight of students in a class.

    • Amount of lemonade in a jug.

Activity: Identify Variable Types

  1. Amount of salt in a glass container: Continuous

  2. Number of pupils joined the Math Club: Discrete

  3. Speed of a Honda Civic car: Continuous

  4. Average weight of 6-year-old children: Continuous

  5. Scores of 100 Grade 11 students in a test: Discrete