Level 1 - Quantitative Method - Introduction to Statistics

Introduction to Statistics

一如以往，我只會go through部分內容，請不要過分依賴

Calculator’s function

計算機上built in了statistics的function，可用作計算Mean, Standard Deviation (S.D.)。Steps:
1.       2ND   7  (DATA)
2.      習慣先clear memory à  2ND   CElC
3.      ↑   ↓  input data à X = observation; Y = frequency
4.       2ND   8  (STAT)
5.      Set mode à  2ND   ENTER  (SET) à 1 – V (one variable)
6.      ↑   ↓  可顯示有關Data 的n, mean, population and sample S.D.

Distribution of Observations

1.      Normal Distribution:

         Features:

          - Symmetric 左右對稱
          - Mean = Median = Mode

2.      Skewness
       在+ve或-ve side有extreme value，令distribution不對稱

        Positive (right) skew vs. Negative (left) skew:

        - Positively(right) skew 指extreme value 在positive/right side à fat tail on the right
         - Negatively(right) skew指extreme value在negative/left side à fat tail on the left

        Mean, Median, Mode之中，mean最受extreme value影響，mode 則最少，所以:
        +ve skewed distribution à mean > median > mode
          -ve skewed distribution à mean < median < mode

Kurtosis

Kurtosis 量度接近中間(area A)，偏離中間(area B)，及 extreme value(area C)的分布

Normal distribution 的 kurtosis 為 3

如果 kurtosis > 3 à leptokurtic distribution:
Area A & C 會比 normal distribution 大;
Area B 會比normal distribution 小
è Extreme value 機會較大

如果kurtosis < 3 àplatykurtic distribution:
Area A & C 會比normal distribution小;
Area B會比normal distribution大
è   Extreme value機會較小

Chebyhev’s Equality

無論distribution是normal，-ve/+ve skewed，leptokurtic/platykurtic，% of observations within ± k個S.D.都不會少於 1 – 1/k²