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