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

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