Statistics

Statistics

1. Measurement Scales

   • QUALITATIVE-Nominal: identity property. Values assignes to variables represent a descriptive category, they have no inherent numerical value with respect to magnitude
     • Gender, religion, cellphone number
   • QUAL-Ordinal: identity and magnitude properties. Each value on the ordinal scale has an unique meaning, an ordered relationship to every other value on the scale
     • Results of horse race, how do you feel today?
   • QUANT-Interval: identity, magnitude, equal intervals properties. To know if different values are bigger or smaller also how much bigger or smaller are.
     • Fahrenheit scale, time of the day on 12 hrs clock
   • QUANTITATIVE-Ratio: identity, magnitude, equal intervals and minimum value of zero identities
     • weight of an object, distance in inches, math class grade, temperature in K, cost in euros

2. Sampling Methods

   • Probability
     • Simple: Random
     • Systematic: choose according to a rule
     • Stratified: groups chosen
     • Cluster: grabbing elements according to some rule
   • Non-Probability
     • -Quota: elements but not randomly chosen
     • Convenience

3. Visual Displays of Data

   • Frecuency Distribution
     • Frecuency: Times an event happens
     • Relative Frecuency: frecuency over total elements in %
     • Data set with large #'s: Grouped Frecuency Distribution
       • 1.Make sure each data item will fit in 1 class
       • Data: lower class limits upper class limits, class width, class mark
       • 2. Try to make all classes, same width
       • 3.Make sure classes don't overlap
       • 4.Use 5-12 classes
   • Displays
     • Line Graph(how quantity changes respect something)
     • Circle Graph (represent total of categories in sections to show magnitudes)
     • Bar Graphs(frecuency distribution of non-numerical observations)
     • Stem and Leaf (numbers grouped, help with big quantities)
     • Histogram(display of data using bars, groups #'s into ranges

4. Measures of Central Tendency

   • Mean
     • -x-(sample) N(population). Addition of all items and then divide this into the # of items
       • -x-=Ex/n
   • Weighted mean
     • -w-=E(x.f)/Ef
       • Sum of all products of items by weighting factors, divided by the sum of all weighting factors
   • Mode
     • Value that occurs more often
   • Median
     • 1.Rank items (least to greates)2. If # is odd, median is at the middle 3.Even #, median is mean of 2 middle items
     • =n+1/2=Ef+1/2

5. Measures of Dispersion

   • Standard deviation: based on deviations from mean of data values
     • Calculate -x-, mean of #'s; Find deviations from -x-; Square each deviation; Sum squared deviations; Divide sum by n-1; Square root of quotient
   • Chevyshev's Teorem: for any set of #'s regardless their distribution, their fraction that lies within K stand. dev. of their mean is at least
     • 1-1/k^2
       • K=# of stand. dev.
   • Range: greatest value-lowest value
   • Coefficient of Variation

6. Measures of position

   • z-score(standard score)
   • Decile
   • Quartile
   • Percentile
   • Box Plot

7. Statistics:search, analize, interpret data

   • Descriptive:recopilation of data
   • Inferential: conclusions from data
   • population: whole data
   • Sample: part of population
   • Random variables
     • Qualitative
       • no numbers
     • Quantitative
       • Discrete(counting)
       • Continuous(measure)

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