MODULE 3

• Polya's Four Steps to Problem Solving

  1. Understand the Problem<|>2. Devise a plan<|>3. Carry out the Plan<|>4. Look Back
• George Polya


  • Father of modern problem solving
  • Studied extensively and wrote numerous mathematical papers and three books about problem solving
• Understand the Problem

  1. Read the problem carefully

  2. List down the components and data involved

  3. Assign variables
• Devise a plan

  1. Set-up the equation

  2. Draw a diagram

  3. Make a chart
• Carry out the Plan

  Solve the equation
• Look Back

  Check if the information in the problem is satisfied
• Intuition


  The ability to understand something instinctively without the need for conscious reasoning
• Mathematical Proof

  An argument which convinces other people that something is true
• Branches of Statistics

  • Descriptive Statistics
  • Inferential Statistics
• Use of Statistics

  • Government
  • Weather Forecast
  • Emergency Preparedness
  • Political Campaigns
  • Healthcare/ Predicting Diseases
  • Sports
  • Research
  • Education
• Data Management


  The development, execution and supervision of plans, policies, programs and practices that control, protect, deliver, and enhance the value of data and information assets
• Data Gathering Methods

  • Direct or Interview Method
  • Indirect or Questionnaire Method
  • Registration Method
  • Experimental Method
  • Observation Method
• Scales of Measurement

  • Nominal
  • Ordinal
  • Interval
  • Ratio
• Data Presentation Methods

  • Textual Form
  • Tabular Form
  • General Form
• Types of Graphical Presentation

  • Line Graph
  • Bar Graph
  • Pie Graph
  • Pictograph
• Ways of Organizing Numerical Data

  • Array
  • Frequency Distribution Table
• Bar Graph


  Used when the height of bars represents quantity or frequency for each category
• Pie Graph

  Used to show percentage or the composition by parts of a whole
• Pictograph


  Used to immediately suggest the nature of data
• Array


  An arrangement of numerical data/values according to order of magnitude either ascending or descending
• Frequency Distribution Table

  A condensed version of an array that categorizes numerical data into intervals or classes
• Parts of a Frequency Distribution Table

  • Classes (mutually exclusive categories defining lower and upper limits with equal intervals)
  • Class Frequency (number of observations in each class)
  • Class Mark or Class Midpoint (used in computing mean and measures of variability)
  • Cumulative Frequency (sum of frequencies in a particular class of interest)
  • Relative Frequency (percentage of observations in a particular class of interest)
• Steps in Constructing a Frequency Distribution with Equal Class Size


  1. Determine the range R of the numerical data

  2. Determine the number of classes K using Sturges' Approximation

  3. Determine the class size C

  4. Determine the lower limit of the first class

  5. Construct the class intervals and determine the class frequencies
• Steps in Constructing Frequency Charts

  1. Label either class limits or class marks along the horizontal axis

  2. Plot the frequency of each class along the vertical axis above the class mark

  3. The vertical scale must always include zero

  4. The horizontal scale must include only the range of the observed data and one extra interval at each end

  5. The vertical axis height should be approximately ¾ the length of the horizontal axis
• Frequency Histogram


  A set of vertical bars whose areas are proportional to the frequencies presented
• Frequency Polygon


  A line chart plotted along the same scale as the histogram, with class frequency plotted against class mark
• Less than Ogive


  The less than cumulative frequency plotted against the upper-class limit
• Greater than Ogive


  The greater than cumulative frequency plotted against the lower-class limit
• Data Analysis and Interpretation is the process of making sense of numerical data that has been collected, analyzed, and presented
• Descriptive Statistics


  Method in describing the characteristics of individual objects or group of individuals under study
• Inferential Statistics

  Analyzing and interpreting data
• Three Methods in Describing a Set of Data


  • Measures of Central Tendency
  • Measures of Dispersion
  • Measures of Skewness and Kurtosis
• Measures of Central Tendency

  Measures indicating the center of a set of data which are arranged in order of magnitude, including mean, median, and mode
• Arithmetic Mean


  The most commonly used measure of central tendency
• Median


  The middle number or the mean of the two middle numbers in a list of numbers arranged in numerical order
• Mode


  The number that occurs most frequently in a list of numbers
• Weighted Mean

  A value used when some data values are more important than others