Math #

• Statistics


  A science that studies data to be able to make decisions. A tool in the decision-making process.
• Statistics as a science


  1. Involves the methods of collecting, processing, summarizing and analyzing data in order to provide answers or solutions to an inquiry

  2. Interpreting and communicating the results of the methods to support a decision that one makes when faced with a problem or inquiry
• Origin of the word "statistics"

  Comes from the word "state" because governments have been involved in statistical activities, especially the conduct of censuses
• Role of the Philippine Statistics Authority (PSA)

  1. Conducts censuses to obtain information about socio-economic conditions in the country

  2. Helps the government make plans, such as how many schools and hospitals to build

  3. Conducts censuses of population, housing, agriculture, and business/industry
• Non-statistical questions


  Questions that could be answered by a piece of information which is considered always true. There is a correct answer based on a fact, and you don't need the process of inquiry to answer.
• Statistical questions


  Questions that need more information or data to be able to answer. Either you need to get observations from all those concerned, or you get representative groups from which you gather your data.
• Statistical question: Do dogs eat more than cats?


  Requires getting the amount of food that all dogs and cats eat, or getting a representative group of dogs and another representative group for the cats and measuring the amount of food each group eats.
• Statistical question: Do math teachers earn more than science teachers?


  Requires getting data on income/wages of either all math and science teachers, or even a sample of these teachers.
• Statistical question: Does it rain more in Davao City than in Marawi City?


  Requires getting rainfall data on the two cities in a reference period.
• Statistical question: What is the proportion of MSU-Marawi Senior High School students who are underweight or overweight for their age?


  Requires getting data on the weights of all students, comparing these weights to a reference weight for student ages, and determining the percentage of students that are underweight or overweight for their age.
• Two general types of statistics


  • Descriptive statistics
  • Inferential statistics
• Descriptive statistics


  Statistics that organize and summarize observations
• Inferential statistics


  Statistics used to interpret the meaning of descriptive statistics
• Descriptive statistics


  • Procedures used to summarize, organize, and make sense of a set of scores or observations
  • Typically presented graphically, in tabular form (in tables) or as summary statistics (single values)
• Inferential statistics


  • Procedures used that allow researchers to infer or generalize observations made with samples to the larger population from which they were selected
• Population


  The totality of the observations of which the study is concerned. The set of all individuals, items, or data of interest.
• Population parameter


  A characteristic (usually numeric) that describes a population
• Sample


  A subgroup of the population. A set of selected individuals, items, or data taken from a population of interest.
• Sample statistic


  A characteristic (usually numeric) that describes a sample
• Variable


  A characteristic that is observable or measurable in every unit of the universe (or population)
• Data


  Facts and figures that are presented, collected, and analyzed. The actual values of variables. Can be numeric or non-numeric and must be contextualized.
• Qualitative variables


  Express a categorical attribute, vary by class
• Quantitative variables


  Vary by amount, also called numerical data
• Discrete data


  Data that can be counted
• Continuous data


  Data that can be measured, e.g. height of a survey respondent
• Scales of measurement


  Refer to how the properties of numbers can change with different uses
• Scales (levels) of measurement


  • Nominal
  • Ordinal
  • Interval
  • Ratio
• Nominal scale


  Categorical and non-numeric, numbers assigned to represent something or someone
• Ordinal scale


  Measurements where values convey order or rank alone
• Interval scale


  Measurements where values have no true zero and the distance between each value is equidistant
• Ratio scale


  Measurements where a set of values has a true zero and are equidistant
• Methods of Collecting Data


  • Interviews
  • Questionnaires
  • Observations
  • Experimentation
  • Use of existing records/data
• Interviews


  Person-to-person encounter between interviewer and interviewee, can be in person or by telephone
• Questionnaires


  Common tool for gathering information, respondents must be available and willing to participate
• Observations


  Appropriate for obtaining data on behavior of individuals or groups, can be direct or indirect
• Experimentation


  Can be applied to obtain data from experiments, advantage is experiments can be repeated
• Use of existing records/data


  Convenient way of obtaining data from public or unpublished documents, or the internet
• Sampling Methods


  • Probability Sampling
  • Non-Probability Sampling
• Methods of Probability Sampling


  • Simple Random Sampling (SRS)
  • Systematic Random Sampling
  • Stratified Random Sampling
  • Cluster Sampling
• Simple Random Sampling (SRS)


  Every subset of size n of the population has an equal chance of being selected