Python_data_science_第一课

####Data Science 打算写一系列的笔记，记录下平时看书，看视频学到的知识.

今天是第一课.

1. Mean, Mode, Median.

    Mean AKA Averate: sum/ number of samples
    Median: sort the values, and take the value at the midpoint, for even numbers
    then take the average of the midpoint 2.
    Mode: the most common value in a data set, which means this data occurs the most time.
   

   下面使用Python 代码来实地求出这些值

    #import packages
    import numpy as np
    from scipy import stats
    import matplotlib.pyplot as plt
   
    #fabricate some data
    #use np.random.normal Draw random samples from a normal (Gaussian) distribution
    incomes = np.random.normal(27000,15000,10000)
    '''
        Parameters
        ----------
        loc : float or array_like of floats
            Mean ("centre") of the distribution.
        scale : float or array_like of floats
            Standard deviation (spread or "width") of the distribution.
        size : int or tuple of ints, optional
            Output shape. If the given shape is, e.g., ``(m, n, k)``, then
            ``m * n * k`` samples are drawn. If size is ``None`` (default),
            a single value is returned if ``loc`` and ``scale`` are both scalars.
            Otherwise, ``np.broadcast(loc, scale).size`` samples are drawn.
    '''
    np.mean(incomes) #average ,close to 27000
    plt.hist(incomes, 50)
    plt.show()
   
    #compute median
    np.median(incomes)
   
    #add one outlier, then the mean will change a lot, but the median will not change too much.
    incomes = np.append(incomes, [1000000000])
    In [26]: np.mean(incomes)
    Out[26]: 126837.27483313478
    In [27]: np.median(incomes)
    Out[27]: 26584.942499458524
   
    #If there is more than one such value, only the smallest is returned.
    lst=[1,1,2,2,3,3,4,4]
    In [20]: stats.mode(lst)
    Out[20]: ModeResult(mode=array([1]), count=array([2]))
    In [15]: lst=[1,2,3,2,2,2]
    In [16]: stats.mode(lst)
    Out[16]: ModeResult(mode=array([2]), count=array([4]))
    ages = np.random.randint(18,high=90, size=500)
    stats.mode(ages)
   

2. standard deviation and variance:

variance: is simply the average of the squared differences from the mean.  
Standard deviation is the squared root of the variance.  

Example:  
what is the variance of (1,4,5,4,8)  
get mean: (4.4)  
differences from the mean: (-3.4, -0.4, 0.6, -0.4, 3.6)  
Squared differences: (11.56, 0.16, 0.36, 0.16, 12.96)  
average of the squared differences:  5.04  
Standard deviation : 2.24   


下面是代码：



    #use numpy to calculate variance and standard deviation.
    In [30]: lst=[1,4,5,4,8]
    #standard deviation
    In [31]: np.std(lst)
    Out[31]: 2.2449944320643649
    #variance
    In [32]: np.var(lst)
    Out[32]: 5.04