MMW

• STATISTICS

  • A mathematical system that involves the collection, organization and analysis of data to create inference.
• Areas of Statistics:

  • Descriptive Statistics – involves the organization and describing data. It involves tables and graphs.
  • Inferential Statistics – involves creating conclusions from the data gathered from the sample.
• Population is the overall collection of targeted subjects.

  Parameter are the value gathered from the population.
• Sample is a subset of the population that will be used in the study. Statistic is a value gathered from the sample
• Variables are the characteristics of an object of interest. It can be either numerical in nature or categorical.
• Attribute is a defined value of the variable
• Quantitative variable presents value in numerical form. It can be either discrete or continuous.

  
  

  Discrete variables are variable that can be counted (number of people or objects).

  Continuous variable are variables that can be measured(height, weight or volume).
• Qualitative variable presents values that are categorical and mathematics is not applied( gender, performance rate or place)
• • Nominal – for qualitative variables. Values that can’t be ranked.(e.g. name or labels)
  • Ordinal - for qualitative variables. Values that can be ranked.(e.g. student year level or pain level)
  • Interval – for quantitative variables. The value of zero is not an absence of value. For example if the temperature is zero degrees Celsius it does not mean no temperature it means it is cold.
  • Ratio – for quantitative variables. The value of zero is absolute. For example distance or height
• DATA COLLECTION

  • Direct Method(interview) – face to face conversation with correspondents
  • Indirect Method(Questionnaire) – a set of questions related to the subject is distributed to the respondents
  • Observation – data from monitoring the subject
  • Experimentations – data from conducting experiments and comparing actual data with control data
• DATA SOURCES

  • Primary Sources – data are directly collected by the researchers. Examples are interviews and questionnaires.
  • Secondary Sources – data collected by other researchers. Examples are articles and journals by other researchers
• • Central tendency is the numerical value that presents the central value of a collection of data
• • Mean is the average value of the data set
  • Median is the middlemost value of the data set arranged in either ascending or descending order. For odd number of values, it is the central value but for even number of values it is the average between the two central values
  • Mode is the value that frequently appear
• Range is the difference between the maximum and minimum values.

  Variance measures the distance between the value and the mean.

  Standard deviation measures the diversion of variables.
• • Frequency dictates how often something happened
  • Frequency distribution shows how the frequency is distributed to the data set
  • Frequency distribution table presents and organizes the data in a tabular form
• SCATTER PLOT

  • Scatter plot shows the direction of relationships between variables.
  • You can determine the strength of the relationship by observing the plot and see how close the points are to a line formation.
• LEAST SQUARES REGRESSION

  • Represents the relationship between variables in a scatter plot
  • y = mx + b
• LINEAR REGRESSION

  • Linear Regression estimates a linear equation to represents dependent and independent variables: y = mx + b
• CORRELATION

  • measures the linear association between two variables, x and y. It has a value between -1 and 1 where:
  • -1 indicates a perfectly negative linear correlation between two variables • 0 indicates no linear correlation between two variables
  • 1 indicates a perfectly positive linear correlation between two variables
• MEASURE OF RELATIVE POSITION

  • Percentile - it is a measure by dividing the distribution by 100 parts
  • Quartiles - it is a measure by dividing the distribution by 4
  • Z score or Standard score - is the number of the standard deviations above or below the mean of the data
• CUMULATIVE FREQUENCY

  • Cumulative frequency is the sum of the previous frequency up to the current frequency
• RELATIVE FREQUENCY

  • shows the proportion of each data to the whole set
• Patterns

  • It is defined as an organization of shapes and symbols distributed in regular interval
• SYMMETRY

  • Symmetry occurs when dividing a figure by two and will produce the two similar figures. Symmetry can be reflective or rotational
• REFLECTIVE SYMMETRY

  • the right half and left half of the figure should be mirror reflection of each other
• ROTATIONAL SYMMETRY

  • if the figure rotates at its center, the figure should be the same as the original
• ORDER OF ROTATIONAL SYMMETRY

  • it is defined by the number of times one can rotate a figure to get the same figure.
  • if the shape is a regular polygon the order depends on the number of sides for example: A rectangle has an order of 2 but a square has an order of 4
• FRACTALS

  • Pattern of infinite iterations of the figure going in a loop
• SPIRAL

  • Coiled pattern revolving about a center point
• WAVES

  • Disturbances that carry energy
• TESSALLATIONS

  • Formed by repeating shapes over a plane.
• CRACKS

  • Openings formed to release stress
• SEQUENCE

  • A list of numbers or elements arranged in a certain pattern.
  • Each elements will be called terms
  • It can be finite or infinite
  • It can be ascending or descending order
  • Each term can be evaluated through direct formula, relations from the preceding term or table of value
• ARITHMETIC SEQUENCE

  • each term have a common difference between their preceding terms
• GEOMETRIC SEQUENCE

  • each term have a common ratio between their preceding terms
• HARMONIC SEQUENCE

  • each term is the reciprocal of the terms in an arithmetic sequence
• QUADRATIC SEQUENCE

  • the difference between the terms are arranged in arithmetic sequence
• TRIANGLE NUMBER SEQUENCE

  • the pattern of these sequence form equilateral triangles
• SQUARE NUMBER SEQUENCE

  • the pattern of these sequence forms squares
• CUBE NUMBER SEQUENCE

  • the pattern of these sequence forms squares