Statistics

Statistics

1. Basics concepts

   • Statistics is the science of collecting, describe, analyze, and interpret data.
     • inferential statistics, has to do with obtaining inferences or conclusions
     • inferential statistics, has to do with obtaining inferences or conclusions
     • A population (or universe) is the totality of the elements or things under consideration.
     • A sample is the portion of the population that is selected for analysis.
     • A parameter is a measure of overview that is calculated to describe a characteristic of a population.
     • A statistic is a measure of overview that is calculated to describe a characteristic of a single sample of the population.
     • random variables
       • Qualitative random variables produce categorical responses, i.e., to describe an element of a population.
       • Quantitative random variables produce numerical answers; quantify an element of the population.
         • Discrete data: are numerical responses arising from a process of counting. Continuous data: are responses arising from a process of measurement.

2. Measurement Scales

   • Properties of Measurement Scales
     • • Identity. • Magnitude. • Equal intervals. • A minimum value of zero.
   • Nominal Scale of Measurement
     • only the identity
       • Qualitative
   • Ordinal Scale of Measurement
     • identity and magnitude.
       • Qualitative
   • Interval Scale of Measurement
     • identity, magnitude, and equal intervals.
       • Quantitative
   • Ratio Scale of Measurement
     • identity, magnitude, equal intervals, and a minimum value of zero.
       • Quantitative

3. Sampling Methods

   • way that observations are selected from a population to be in the sample for a sample survey
     • population parameter: true value of population attribute
     • sample statistic: an estimate based on sample data, of a population parameter
     • sampling method categories
       • probability
         • simple:(random) systematic:(element according to one rule) stratified:(characteristics divided in groups) cluster:(groups taken but no separated )
       • non probability
         • quota:(like cluster with an specific characteristic) convenience:(easy elements)

4. Visual displays of data

   • Displays
     • line graphs
     • circle graphs
     • bar graphs
     • stem and leaf
     • histogram
   • Frequency Distribution
     • Frequency: list different values among their frequencies
     • Relative Frequency: fraction or % of the data set represented by the item
     • data with large numbers
       • groupes frecuency distribution
         • data: lower class limits ,upper class limits, class width class mark

5. Measures of cent ran tendency

   • Median
     • *is not so sensitive to extreme values *divides a group of numbers into 2 parts , with half the numbers below the median and a half above it
       • odd=middle even=mean of 2 middle terms
   • Mode
     • the value that occurs most often
   • Mean
     • (average), the most common measure of the central tendency
   • Weighted mean

6. Measures of dispersions

   • coefficient of variation
   • chevyshev`s theorem
   • range
   • standard deviation

7. Measures of position

   • Decile
     • nine values of a variable, which divides its distribution into ten parts with equal frequencies
       • D1, D2, D3, D4, D5, D6, D7, D8, and D9.
   • Quartile
     • the three points that divide the data set into four equal groups.
       • The lower quartile (Q1) is the median of the lower half of the data set.
       • The upper quartile (Q3) is the median of the upper half of the data set.
   • Percentile
     • the value below which a percentage of data falls.
   • Box plot
     • graphically depicting groups of numerical data through their quartiles

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