matm

• Statistics


  A collection of methods for planning experiments, obtaining data, and then analyzing, interpreting and drawing conclusions based on the data
• Descriptive statistics


  • Summarizes or describes the important characteristics of a known set of data
• Inferential statistics


  • Uses sample data to make inferences about the population. It consists of generalizing from samples to population, performing hypothesis testing, determining relationships among variables, and making predictions
• Descriptive statistics example


  • Last semester, the ages of students at a certain college ranged from 16 to 25 years old
• Inferential statistics example


  • A recent study showed that eating garlic can lower blood pressure
• Data


  Data in statistics is always a result of experiment, observation, investigation and other means and often appears as a numerical figure and then evaluated to make it into useful knowledge
• Sources of data


  • Survey
  • Experiment
  • Investigation
• Quantitative (Numerical) data


  • Continuous variables - values obtained by measuring, all of which cannot be put into a list because they can have any value in some interval of real numbers
  • Discrete data - values obtained by counting

  
• Qualitative (Categorical) data


  • Nominal - classifies elements into two or more categories or classes, the numbers indicating that the elements are different but not according to order or magnitude
  • Ordinal - scale that ranks individual in terms of the degree to which they possess a characteristic of interest

  
• Scales of measurement


  • Nominal
  • Ordinal
  • Interval
  • Ratio

  
• Nominal scale


  A non-numeric label or numeric code may be used. Data are labels or names used to identify an attribute of the element
• Ordinal scale


  A non-numeric label or numeric code may be used. The data have the properties of nominal data and the order or rank of the data is meaningful
• Interval scale


  Interval data are always numeric. The data have the properties of ordinal data, and the interval between observations is expressed in terms of a fixed unit of measure
• Ratio scale


  The data have all the properties of interval data and the ratio of two values is meaningful. Variables such as distance, height, weight, and time use the ratio scale. This scale must contain a zero value that indicates that nothing exists for the variable at the zero point

  
• Data can be qualitative or quantitative. The appropriate statistical analysis depends on whether the data for the variable are qualitative or quantitative. There are more options for statistical analysis when the data are quantitative
• Population


  Defined as groups of people, animals, places, things or ideas to which any conclusions based on characteristics of a sample will be applied
• Sample


  A subgroup of the population
• Parameter


  A numerical measure that describes a characteristic of the population
• Statistic


  Numerical measure that is used to describe a characteristic of a sample
• Measures of central tendency

  • Mean (x) - arithmetic average
  • Median (Md) - middle value in an ordered array
  • Mode (Mo) - highest frequency

  
• Mean


  The sum of all the values in the observation or a dataset divided by the total number of observations. This is also known as the arithmetic average

  
• Properties of mean


  • Can be applied for interval or ratio data
  • A set of data has only one mean
  • All values are included in computing the mean
  • Mean is very useful in comparing two or more data
  • Mean is affected by extremely small or large data set

  
• Properties of median


  • The median is unique, there is only one median
  • Median is not affected by the extremely small or large values
  • Median can be applied for ordinal, interval and ratio data
• Properties of mode


  • Mode is found by locating the most frequently occurring value
  • Mode is he easiest average to compute
  • There can be more than one mode or no mode
  • Mode is not affected by extremely small or large values
  • Mode can be applied for nominal, ordinal, interval or ratio data
• Types of data


  • Ungrouped Data
  • Grouped Data
• Frequency distribution table


  A device for organizing and presenting grouped data. If the data contains 30 cases or more, a frequency distribution table may be constructed to make the task more manageable and to save time in calculating different statistics

  
• Ungrouped frequency distribution example

  • Midyear Test Scores of 45 Students in Statistics
• Grouped frequency distribution example

  • Midyear Test Scores of 45 Students In Statistics
• Calculating median


  First get the value of N/2 to determine the row where the median is located. Choose the <cf closest to N/2 but not lower

  
• Calculating mode


  Locate the class with the highest frequency
• Statistics itself came from the Latin word "status" which means state. From the ancient times, statistics was used by state leaders to know how much tax to levy their subjects and how many soldiers are needed in an expected war
• In capitalism, not only the leaders of the state but also capitalists, are interested in statistical surveys resulting to increased demand for data processing for their increasing benefits such as insurance
• For most people, "statistics" is a scary thing that must be avoided as much as possible because they think that it is a collection of numbers and vague formulas. People, without noticing, applies statistics in their everyday life, such as to the amount of food they eat, how much money was in their purse, how far is their work area to respective homes, color of their hair, number of rebounds and assists of a player in a basketball game, their height and weight
• In the past, statistics was used by state leaders to know how much tax to levy their subjects and how many soldiers are needed in an expected war
• Data in statistics


  Always a result of experiment, observation, investigation and other means and often appears as a numerical figure and then evaluated to make it into useful knowledge
• For most people, "statistics" is a scary thing that must be avoided as much as possible because they think that it is a collection of numbers and vague formulas
• People, without noticing, applies statistics in their everyday life, such as to the amount of food they eat, how much money was in their purse, how far is their work area to respective homes, color of their hair, number of rebounds and assists of a player in a basketball game, their height, gender, and so on
• Statisticians


  Develop and apply appropriate methods in collecting and analyzing data. They guide the design of the research study and then analyze the results. The interpretation of the result is the basis of the statistician in making inferences about the population
• Descriptive Statistics


  Deals with the collection and presentation of data and collection of summarizing values to describe its group characteristics. The most common summarizing values are the measure of central tendency and variation

  
• Inferential Statistics


  Deals with the predictions and inferences based on the analysis and interpretation of the results of the information gathered by the statistician. Some of the common statistical tools of inferential statistics are the t-test, z-test, analysis of variance, chi-square, and Pearson r