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Statistics: collecting, analyzing, presenting, interpreting, and making…

- - - - Median= The middle value of an ascending ordered data set.
        
        Odd number of data (n): Median is the middle number
        
        Even Number of Data(n): the two middle number divided by two (the average of two middle numbers)
      - Mean: (Sum of all values)/(Number of values)
        
        Mean for sample data: x̄(x-bar) = Σx/N (N is population)
        
        Mean for population data: µ(mu) =Σx/n (n is sample size
      - Mode: The value in data set that occurs with the highest frequency.
        
        data set with no mode: [13,4,55,6,7,8]
        
        data set with two mode: [13,4,5,6,7,5,4]
        
        data set with three mode: [4,5,6,10,15,5,10,6]
      - relationship among Mean, Median, and Mode
        
        Symmetric histogram: mean, median and mode all occur identical at the center of distribution.
        
        Skewed to the right: the value of the mean is the largest, the mode is smallest and median occur in between.
        
        Skewed to the left: Value of the mean is the smallest and mode is the largest and median in the middle.
    - - Range: Largest Value - Smallest Value
      - Standard Deviation: how spreader data is around the mean. lower std tells the data is spread relatively smaller range around the mean. for higher std is the opposite.
        
        Variance: distance of data points from the mean
        
        Population Variance: σ sq 2 = (Σ(x- µ)sq 2)/N
        
        shortcut formula: σ2 = (Σx2 - ((Σx)2)/N)N
        
        sample variance: s sq 2 = (Σ(x- x̅)sq 2)/n-1
        
        s2 = (Σx2- ((Σx)2)n)n-1
        
        STD
        
        Population STD (square root of variance): σ = ((Σ(x- µ)sq 2)/N) sqr 2
        
        σ = ((Σx2 - ((Σx)2)/N)N)sqr 2
        
        sample STD (square root of variance): s= ((Σ(x- x̅)sq 2)/n-1) sqr 2
        
        s = ((Σx2- ((Σx)2)n)n-1)/sqr 2
  - - - µ = Σmf/N (m midpoint of the class, and f frequency of the class)
      - x̅ = Σmf/n
    - - Population Variance: σ2 = (Σ(m - µ)2)/N
        
        σ2 = (Σm2f - ((Σmf)2)/N)N
      - sample variance: s sq 2 = (Σ(m - x̅)sq 2)/n-1
        
        s2 = (Σm2f - ((Σmf)2)n)n-1
    - - σ = ((Σ(m- µ)sq 2)/N) sqr 2
        
        σ = ((Σm2f - ((Σmf)2)/N)N)sqr 2
      - s= ((Σ(m- x̅)sq 2)/n-1) sqr 2
        
        s = ((Σm2f- ((Σmf)2)n)n-1)/sqr 2
      - Empirical rules: bell-shape or normal distribution
        
        68% of the observation lie within one standard deviation of the mean.
        
        95% of the observation lie within two std of the mean.
        
        99.7 of the observation lie within three std of the mean.
  - - - Q2: The second quartile is median of a data set
      - Q1: middle point between value less than median.
      - Q3: middle point between values greater than median of dataset.
      - IQR: The diference between third quartile and first quartile. IQR = Q3-Q1
      - Box-and-Whisker plot: A plot that shows the center, spread, and skewness of a data set. a box and two whisker that use median, Q1,Q3 for box, and highest and lowest value for whiskers.
    - - Calculating percentile: Pk = value of the (kn/100) th term in a ranked data set.
      - percentile rank of a value: Xi = Number of values less than Xi / total number of values in the data set
- - - - census a survey that include every member of population
    - - census every member of population
        
        sample survey: A survey that include portion of the population
        
        Representative Sample: A sample that represent characteristics of population as close as possible
        
        Random Sample: each member has fair and equal chance to be selected.
- - - - type of variables
        
        Quantitative Variables: can be measure numerically, data is quantitative data
        
        Discrete Variable: countable value such as number of houses, cars etc.
        
        Continuous Variable: can assume any numerical value over a certain interval such as length, age, time etc
        
        Quantitative Data
        
        Frequency Distribution: List all the classes and number of values that belong to each class. data presented in form of frequency distributions are called grouped data
        
        Class boundary: A class boundary is given by the midpoint of the upper limit of one class and the lower limit of the next class
        
        Class Width = upper boundary - lower boundary
        
        class midpoint = (lower limit + upper limit)/2
        
        Constructing Frequency distribution Table
        
        Calculating of Class Width : approximate class width = (Largest Value - Smallest Value)/number of classes
        
        Relative frequency and percentage distribution
        
        relative frequency of a class = frequency/(sum of all frequency) = f/sigmaf
        
        percentage: (relative frequency) * 100%
        
        histogram: class on xaxis, frequency on yaxis
        
        shape of histogram
        
        3 more items...
        
        Polygon: joining the middle point of each class with straight lines.
        
        Single-valued class: when the value of class is discrete not interval we can construct class with single value. such vehicle owned by household. 0 vehicle class, 2 vehicle class, 5 vehicle class etc.
        
        Cumulative Frequency Distribution: total numbers of value that fall bellow the upper boundary of each class.
        
        cumulative relative frequency = (cumulative frequency of a class )/total observation in the data set
        
        Percentage = (cumulative relative frequency) * 100%
        
        Ogive: is a curve drown for the cumulative frequency distribution by joining by the straight line with dot equal to cumulative frequency of respective classes
        
        Stem-and-Leaf display: each value divided into two portion; stem and leaf. p58
        
        Dotplots:
        
        Outlier or Extreme Values: Values that are very small or very large relative to the values in dataset.
        
        qualitative or categorical variables: variable that cannot assume numerical value but can be classified such as gender, maker of computers etc.
        
        Qualitative Data
        
        Frequency distributions: list all the categories and number of elements belong to that catagories
        
        Analyzing
        
        percentage: (relative frequency) * 100%
        
        angel size(pie chart): (relative frequency) * 100%
        
        relative frequency: (frequency of that catagory)/sum of all frequencies
        
        Visualization
        
        Bar Graph: A graph made of bars whose heights represent the frequencies of respective catagories is called bar graph
        
        Pie Char: a circle divided into portions that represent relative frequencies or percentage of a population or sample.
    - - cross-section: data collected on different element at the same time such as revenue of different company in 2020
      - Time-Series: data collected on the same element on different time. such as user traffic in a website on different time of the day