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    Eda Formulas

    Uploaded by

    Lee Angus Santos
    1. The document summarizes key concepts in descriptive statistics and probability distributions. It defines terms like range, mean, median, mode, and standard deviation. 2. Probability concepts like permutations, combinations, and additive/multiplicative rules are outlined. Discrete and continuous probability distributions are introduced. 3. Specific distributions like the binomial and Poisson are defined by their probability mass functions. The mean and variance of the binomial distribution are given as μ = np and σ2 = npq.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Eda Formulas

    Uploaded by

    Lee Angus Santos
    19 views2 pages
    1. The document summarizes key concepts in descriptive statistics and probability distributions. It defines terms like range, mean, median, mode, and standard deviation. 2. Probability concepts like permutations, combinations, and additive/multiplicative rules are outlined. Discrete and continuous probability distributions are introduced. 3. Specific distributions like the binomial and Poisson are defined by their probability mass functions. The mean and variance of the binomial distribution are given as μ = np and σ2 = npq.

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    eda formula

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    EDA-FORMULAS

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    1. The document summarizes key concepts in descriptive statistics and probability distributions. It defines terms like range, mean, median, mode, and standard deviation. 2. Probability concepts like permutations, combinations, and additive/multiplicative rules are outlined. Discrete and continuous probability distributions are introduced. 3. Specific distributions like the binomial and Poisson are defined by their probability mass functions. The mean and variance of the binomial distribution are given as μ = np and σ2 = npq.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    19 views2 pages

    Eda Formulas

    Uploaded by

    Lee Angus Santos
    1. The document summarizes key concepts in descriptive statistics and probability distributions. It defines terms like range, mean, median, mode, and standard deviation. 2. Probability concepts like permutations, combinations, and additive/multiplicative rules are outlined. Discrete and continuous probability distributions are introduced. 3. Specific distributions like the binomial and Poisson are defined by their probability mass functions. The mean and variance of the binomial distribution are given as μ = np and σ2 = npq.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    Chapter 1: DESCRIPTIVE STATISTICS

    𝑹𝒂𝒏𝒈𝒆 (𝑹) = 𝑙𝑎𝑟𝑔𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 – 𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒


    𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑙𝑎𝑠𝑠𝑒𝑠 (𝒎) = 1 + 3.3 log 𝑛 ; 𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑠𝑒𝑠
    R
    class size (𝐜) =
    m
    STEM AND LEAF DISPLAY
    1. Select one or more leading digits for the stem values. The remaining digits become the leaves.
    2. List all the possible stem values in a vertical column.
    3. Record the leaf for every observation beside the corresponding stem value.
    4. Indicate the units for stems and leaves someplace in the display.
    A display having between 5 and 20 stems is recommended
    MEAN MEDIAN MODE VARIANCE
    𝑓𝑖 𝑥𝑖 𝑛 𝑑 1 (∑ 𝑓𝑖 𝑥𝑖 )2
    [ – (𝛴𝑓)𝐿 ] 𝑐 1 𝑠2 = [∑ 𝑓𝑖 𝑥𝑖2 − ]
    𝒙̅=∑ ̃ = 𝐿𝑚 +
    𝒙 2 ̂
    𝒙 = 𝐿 𝑚𝑜 + ( ) 𝑐 𝑛 − 1 𝑛
    𝑛 𝑓𝑚 𝑑 1 + 𝑑 2 ∑ 𝑓𝑖 (𝑥𝑖 − 𝑥̅ ) 2

    𝑤ℎ𝑒𝑟𝑒, 𝐿_𝑚= lower class boundary of the 𝐿𝑚𝑜= lower class boundary of the 𝑆2 =
    modal class 𝑛−1
    𝑙𝑜𝑤𝑒𝑟 𝑙𝑖𝑚𝑖𝑡 + 𝑢𝑝𝑝𝑒𝑟 𝑙𝑖𝑚𝑖𝑡 median class
    𝑥𝑖 = (𝛴𝑓)𝐿 =sum of frequencies of all 𝑑1 = excess of modal frequency of
    2 STANDARD DEVIATION
    classes lower than the median class the next lower class
    𝑓𝑖 = 𝑐𝑙𝑎𝑠𝑠 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑑2 = excess of modal frequency of 𝑠 = √𝑠 2
    𝑓_𝑚= frequency of the median class
    C = size of the median class the next higher class
    𝑐 = size of the modal class interval
    Chapter 2: PROBABILITY
    Permutation can be represented in many ways; these are as follows:
    [𝑃(𝑛, 𝑘)] [𝑃𝑘𝑛 ] [nPk] [𝑃𝑛, 𝑘 ] [nPk]
    1. The number of permutations of n distinct objects taken n at a time is 𝑃 = 𝑛! (𝑤𝑒 𝑠𝑎𝑦 𝑛! 𝑎𝑠 "𝑛 𝑓𝑎𝑐𝑡𝑜𝑟𝑖𝑎𝑙)
    𝑛! = 𝑛(𝑛 − 1)(𝑛 − 2)(𝑛 − 3) ⋯ (2)(1)
    𝑛!
    2. The number of permutations of n distinct objects taken 𝑟 at a time is 𝑃 = 𝑛𝑃𝑟 = (𝑛−𝑟)!
    3. The number of permutations of n objects of which 𝑛1 are identical, 𝑛2 are identical, … , 𝑛𝑚 are identical is
    𝑛!
    𝑃=
    𝑛1 ! ∙ 𝑛2 ! ∙ ⋯ ∙ 𝑛𝑚 !

    The number of combinations of n Properties of Probability


    objects taken r at a time has the formula
    𝑛! 𝑛𝑃𝑟
    1. Positiveness 2. Certainty
    𝑛
    𝑛𝐶𝑟 = ( ) = = 0 ≤ P(A) ≤ 1 P(S) = 1, the probability of a sure event
    𝑟 𝑟! (𝑛 − 𝑟)! 𝑟!

    Additive Rules Conditional Probability


    1. 𝐼𝑓 𝐴 & 𝐵 𝑎𝑟𝑒 𝑎𝑛𝑦 𝑡𝑤𝑜 𝑒𝑣𝑒𝑛𝑡, 𝑡ℎ𝑒𝑛, The conditional probability of A is given that B has
    𝑷(𝑨 ∪ 𝑩) = 𝑷(𝑨) + 𝑷(𝑩) – 𝑷(𝑨 ∩ 𝑩) occurred is defined by
    2. 𝐼𝑓 𝐴 & 𝐵 𝑎𝑟𝑒 𝑚𝑢𝑡𝑢𝑎𝑙𝑙𝑦 𝑒𝑥𝑐𝑙𝑢𝑠𝑖𝑣𝑒 𝑒𝑣𝑒𝑛𝑡𝑠, 𝑡ℎ𝑒𝑛 𝑨 𝑷(𝑨 ∩ 𝑩)
    𝑷(𝑨 ∪ 𝑩) = 𝑷(𝑨) + 𝑷(𝑩) 𝑷 (𝑩) =
    3. 𝐼𝑓 𝐴 𝑎𝑛𝑑 𝐴’ 𝑎𝑟𝑒 𝑐𝑜𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 𝑒𝑣𝑒𝑛𝑡𝑠, 𝑡ℎ𝑒𝑛 𝑷(𝑩)
    𝑷(𝑨) + 𝑷(𝑨’) = 𝟏
    𝐴𝑙𝑠𝑜, 𝑷(𝑨 ∪ 𝑩) – 𝑷(𝑨) = 𝑷(𝑩) – 𝑷(𝑨 ∩ 𝑩) = 𝑷(𝑩 ∩ 𝑨’)

    Multiplicative Rule Independent Events


    If the events A and B can both occur, then Two events A & B are independent if and only if
    𝑨 𝑨 𝑩
    𝑷 ( 𝑨 ∩ 𝑩 ) = 𝑷 ( ) · 𝑷(𝑩) 𝑷 ( ) = 𝑷(𝑨) 𝒂𝒏𝒅 𝑷 ( ) = 𝑷(𝑩)
    𝑩 𝑩 𝑨
    Since P (A^B) = P (B^A), then So that
    𝑩 𝑷(𝑨 ∩ 𝑩) = 𝑷(𝑨) · 𝑷(𝑩)
    𝑷 ( 𝑨 ∩ 𝑩 ) = 𝑷 ( ) · 𝑷(𝑨)
    𝑨

    Chapter 3: PROBABILITY DISTRIBUTIONS


    Properties of a discrete The cumulative distribution function (cdf) The function f(x) is a probability density function (pdf) for a
    probability function F(x) for a discrete random variable X is defined by continuous random variable X, defined over the set of real
    1. 𝑓(𝑥) ≥ 0 𝐹(𝑥) = 𝑃 ( 𝑋 ≤ 𝑥 ) = 𝛴 𝑓(𝑢) numbers R.
    2. 𝛴 𝑓(𝑥) = 1 𝑢≤𝑥 1. 𝑓(𝑥) ≥ 0
    ∞
    2. ∫−∞ 𝑓(𝑥)𝑑𝑥 = 1
    𝑏
    3. 𝑃(𝑎 < 𝑋 < 𝑏) = ∫𝑎 𝑓(𝑥)𝑑𝑥

    Chapter 4: SOME DISCRETE PROBABILITY DISTRIBUTIONS


    the number of success in n independent trials is The mean and variance of the binomial distribution are
    𝑓(𝑥) = 𝑏 (𝑥 ; 𝑛 , 𝑝) = 𝑛 𝐶𝑥 𝑝 𝑥 𝑞 𝑛−𝑥 µ = 𝑛𝑝 𝑎𝑛𝑑 𝜎 2 = 𝑛𝑝𝑞
    Poisson random variable

    the number of the trial on which the kth success occurs, is given by
    𝑓(𝑥) = 𝑏 ∗ (𝑥; 𝑘, 𝑝) = 𝑥−1 𝐶𝑘−1 𝑝 𝑘 𝑞 𝑥−𝑘

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