MATH

• The following are the ages of 15 Grade 10 students who will attend the moving up ceremony: 15, 16, 15, 14, 16, 14, 16, 16, 17, 17, 16, 16, 16, 17, 15
• A junior high school mathematics teacher conducted a long exam for his class of 30 students. The exam coverage included the different measures of central tendency, variability, and location.
• The following table shows the scores of the students in the exam

  
• Measures of Position


  Also known as fractiles, refer to the values or cut-off points for which a specified fraction or percentage of the sample, observations, or distribution reaches a particular probability
• Measures of Location


  Help describe the position of an individual in a certain group
• Quartile


  Score points which divide the data set into FOUR EQUAL PARTS or SUBGROUPS
• First Quartile (Q1)


  The value that separates the lower 25% to larger 75 % of the scores
• Third Quartile (Q3)


  The value that separates the lower 75% to larger 25 % of the scores
• Second Quartile (Q2)


  The median of the data set
• Computing the Quartiles of Ungrouped Data

  1. Rank the data set

  2. Find the median of the data set to locate the Second Quartile (Q2)

  3. Obtain the median of the data set from the least value to the median or Q2 to locate the first quartile, Q1 and the median of the data set from the greatest or highest value to the median to locate the third quartile Q3
• How to compute for the kth quartile


  𝑄𝑘 = 𝑘(𝑛 + 1)4𝑡ℎ 𝑡𝑒𝑟𝑚
• Rank the data set from lowest to highest: 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17
• The quartiles can identify the lower 25% and the upper 25% of the distribution. Implicitly, it also gives the middle 50% of the distribution.
• Grouped Frequency Distribution or Grouped Data

  Data that has been bundled together in categories or classes that are more than one unit in width
• Class Limit


  The minimum value and the maximum value that the class interval may contain
• Lower Class Limit


  The smallest data value that can go into the class
• Upper Class Limit


  The largest data value that can go into the class
• The frequency distribution table below shows the summative Mathematics test results of 40 students.
• Solve for the first, second, and third quartile using the formula
• Outlier


  An extreme observation that lies in an unusual distance from other values in a given set or random sample from a population
• Outliers can influence the mean and standard deviation of the distribution. Some sources of outliers are observational, measurement, or recording error; obtained incorrectly from a wrong sample or population; or might be taken by chance.
• Interquartile Range (IQR)


  A statistical measure of variability computed by subtracting the first quartile from the third quartile
• Research


  A scientific investigation of phenomena which involves a systematic process such as gathering, collecting, presenting, analyzing, and interpreting data to generate new ideas and conclusions for the advancements of the body of knowledge
• Kinds of Research


  • Quantitative Research
  • Qualitative Research
• Quantitative Research


  • Uses numbers to describe and make generalizations about a certain population
  • Types include descriptive, correlational, quasi-experimental, and experimental
  • Characterized by methods and data gathering involving measurable characteristics, standardized instruments, data presentation using graphs/tables/texts, larger sample sizes with random sampling, can be repeated/replicated, emphasizes proof rather than discovery
• Qualitative Research


  • An inquiry process of understanding social or human problems, events, groups, and social interactions by studying how things occur
  • Uses words to describe and generalize results
  • Types include phenomenology, ethnography, grounded theory, and case study
  • Methods include observation, in-depth interviewing, focus group discussion, content analysis, narratology, and analysis of videos and photographs
• Common Types of Research Design or Methods

  • Experimental Research
  • Correlational Research
  • Causal-Comparative Research
  • Survey Research
  • Ethnographic Research
  • Historical Research
  • Action Research
• Experimental Research


  • The researcher has control of the situation by establishing varied treatments and studying the effects
  • Types include pre-experimental, true experimental, and quasi-experimental
• Correlational Research


  • Used to determine the relationship between two or more variables and explore implications for cause and effect
  • Types include bivariate correlational studies, prediction studies, and multiple regression prediction studies
• Causal-Comparative Research


  Intended to determine the cause or the consequences of the differences between groups of people
• Survey Research


  Used to obtain data on specific characteristics of a certain group or population, often through interview, asking the same set of questions, and using survey questionnaires
• Ethnographic Research


  Emphasizes documentation of everyday experiences of individuals in a certain place, through immersion, observation, and interview methods
• Historical Research


  Focuses on studying some aspects of the past, by carefully studying and perusing relevant documents or by interviewing individuals who lived during those times
• Action Research


  A research design that involves the process of systematic inquiry that seeks improvement on social issues affecting the lives of everyday people
• Example 1: Identify the most appropriate research design

  • In and Out of the 4W: Analyzing Junior High School Students' Academic Performance in a Flipped Math Class - Action Research
  • The Effects of GeoGebra to the Mathematical Understanding of Senior High School Students - Experimental Research
  • Lived-experience of Low-Performing Students in Statistics - Qualitative Research (Phenomenological)
• Variable


  Any quantity or quality that can assume any value, level, degree, scale, or magnitude under different conditions
• Types of Variables


  • Independent Variable
  • Dependent Variable
  • Control Variable
  • Intervening Variable
  • Confounding Variable
• Independent Variable


  The cause or stimulus chosen and manipulated by the researcher to determine relationships in an observed phenomenon
• Dependent Variable


  The effect or response variable being tested and measured in an experiment
• Control Variable


  A special type of independent variable that the researcher can manage by controlling or neutralizing the effects of by eliminating or removing such variable