3.11. Series Statistics

import pandas as pd
import numpy as np

s = pd.Series(
    data = [1.0, 2.0, 3.0, np.nan, 5.0],
    index = ['a', 'b', 'c', 'd', 'e'])

s
# a    1.0
# b    2.0
# c    3.0
# d    NaN
# e    5.0
# dtype: float64

3.11.1. Count

• Series.count() - Number of non-null observations

len(s)          # 5
s.size          # 5
s.count()       # 4
s.nunique()     # 4

s.values_count()
# 5.0    1
# 3.0    1
# 2.0    1
# 1.0    1
# dtype: int64

3.11.2. Sum

• Series.sum() - Sum of values

• Series.cumsum() - Cumulative sum

s.sum()
# 11.0

s.cumsum()
# a    1.0
# b    3.0
# c    6.0
# d    NaN
# e    11.0
# dtype: float64

3.11.3. Product

• Series.prod() - Product of values

• Series.cumprod() - Cumulative product

s.prod()
# 30.0

s.cumprod()
# a    1.0
# b    2.0
# c    6.0
# d    NaN
# e    30.0
# dtype: float64

3.11.4. Extremes

• Series.min() - Minimum value

• Series.idxmin() - Index of minimum value (Float, Int, Object, Datetime, Index)

• Series.argmin() - Range index of minimum value

• Series.cummin() - Cumulative minimum

• Series.max() - Maximum value

• Series.idxmax() - Index of maximum value (Float, Int, Object, Datetime, Index)

• Series.argmax() - Range index of maximum value

• Series.cummax() - Cumulative maximum

Code 3.165. Minimum, index of minimum and cumulative minimum

s.min()
# 1.0

s.idxmin()
# 'a'

s.argmin()
# 0

s.cummin()
# a    1.0
# b    1.0
# c    1.0
# d    NaN
# e    1.0
# dtype: float64

Code 3.166. Maximum, index of maximum and cumulative maximum

s.max()
# 5.0

s.idxmax()
# 'e'

s.argmax()
# 4

s.cummax()
# a    1.0
# b    2.0
# c    3.0
# d    NaN
# e    5.0
# dtype: float64

3.11.5. Average

Code 3.167. Arithmetic mean of values

s.mean()
# 2.75

Code 3.168. Arithmetic median of values

s.median()
# 2.5

Code 3.169. Mode

s.mode()
# 0    1.0
# 1    2.0
# 2    3.0
# 3    5.0
# dtype: float64

Code 3.170. Rolling Average

s.rolling(window=2).mean()
# a    NaN
# b    1.5
# c    2.5
# d    NaN
# e    NaN
# dtype: float64

Figure 3.18. Rolling Average

3.11.6. Distribution

Code 3.171. Absolute value

s.abs()
# a    1.0
# b    2.0
# c    3.0
# d    NaN
# e    5.0
# dtype: float64

Code 3.172. Standard deviation

s.std()
# 1.707825127659933

Figure 3.19. Standard Deviation

Code 3.173. Mean absolute deviation

s.mad()
# 1.25

Code 3.174. Standard Error of the Mean (SEM)

s.sem()
# 0.8539125638299665

Figure 3.20. Standard Error of the Mean (SEM)

Code 3.175. Skewness (3rd moment)

s.skew()

Figure 3.21. Skewness

Code 3.176. Kurtosis (4th moment)

s.kurt()

Figure 3.22. Kurtosis

Code 3.177. Sample quantile (value at %). Quantile also known as Percentile.

s.quantile(.3)
# 1.9

s.quantile([.25, .5, .75])
# 0.25    1.75
# 0.50    2.50
# 0.75    3.50
# dtype: float64

Code 3.178. Variance

s.var()
# 2.9166666666666665

Code 3.179. Correlation Coefficient

s.corr(s)
# 1.0

Figure 3.23. Correlation Coefficient

3.11.7. Describe

s.describe()
# count    4.000000
# mean     2.750000
# std      1.707825
# min      1.000000
# 25%      1.750000
# 50%      2.500000
# 75%      3.500000
# max      5.000000
# dtype: float64

3.11.8. Assignments

Todo

Create assignments