Statistics¶

import numpy as np 

# 1D array 
A = np.arange(20)
print(A)

A.ndim

# 2D array 
A2 = np.array([[11, 12, 13], [21, 22, 23]])
print(A2)

A2.ndim

Sum¶

Sum of array elements over a given axis.
- Syntax: np.sum(array); array-wise sum
- Syntax: np.sum(array, axis=0); row-wise sum
- Syntax: np.sum(array, axis=1); column-wise sum

Axis 0 is thus the first dimension (the “rows”), and axis 1 is the second dimension (the “columns”)

# sum of 1D array 
np.sum(A1)

# array-wise sum of 2D array 
np.sum(A2)

# sum of 2D array(axis=0, row-wise sum)
np.sum(A2, axis=0)

# sum of 2D array(axis=1, column-wise sum)
np.sum(A2, axis=1)

Compute the median along the specified axis.
Returns the average of the array elements. The average is taken over the flattened array by default, otherwise over the specified axis. float64 intermediate and return values re used for integer inputs.
- Syntax: np.mean(array); array-wise mean
- Syntax: np.mean(array, axis=0); row-wise mean
- Syntax: np.mean(array, axis=1); column-wise mean

# compute the average of array `A`
np.mean(A)

# mean of 2D array(axis=0, row-wise)
np.mean(A2, axis=0)

# mean of 2D array(axis=1, column-wise)
np.mean(A2, axis=1)

Compute the median along the specified axis.
Returns the median of the array elements.
- Syntax: np.median(array); array-wise median
- Syntax: np.median(array, axis=0); row-wise median
- Syntax: np.median(array, axis=1); column-wise median

# compute the meadian of `A`
np.median(A)

# median of 2D array(axis=0, row-wise)
np.median(A2, axis=0)

# median of 2D array(axis=1, column-wise)
np.median(A2, axis=1)

Return the minimum of an array or minimum along an axis.
- Syntax: np.min(array); array-wise min
- Syntax: np.min(array, axis=0); row-wise min
- Syntax: np.min(array, axis=1); column-wise min

# minimum value of `A`
np.min(A)

# minimum value of A2(axis=0, row-wise)
np.min(A2, axis=0)

# minimum value of A2(axis=1, column-wise)
np.min(A2, axis=1)

Return the maximum of an array or minimum along an axis.
- Syntax: np.max(array); array-wise max
- Syntax: np.max(array, axis=0); row-wise max
- Syntax: np.max(array, axis=1); column-wise max

# maxiumum value of `A`
np.max(A)

# maxiumum value of A2(axis=0, row-wise)
np.max(A2, axis=0)

# maxiumum value of A2(axis=1, column-wise)
np.max(A2, axis=1)

r = np.max(A) - np.min(A)
print(r)

Compute the standard deviation along the specified axis.
Returns the standard deviation, a measure of the spread of a distribution, of the array elements. The standard deviation is computed for the flattened array by default, otherwise over the specified axis.
- Syntax: np.std(array); array-wise std
- Syntax: np.std(array, axis=0); row-wise std
- Syntax: np.std(array, axis=1); column-wise std

# compute the standard deviation of `A`
np.std(A)

# standard deviation of 2D array(axis=0, row-wise)
np.std(A2, axis=0)

# standard deviation of 2D array(axis=1, column-wise)
np.std(A2, axis=1)

Compute the variance along the specified axis.
Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis.
- Syntax: np.var(array); array-wise var
- Syntax: np.var(array, axis=0); row-wise var
- Syntax: np.var(array, axis=1); column-wise var

# compute the variance of `A`
np.var(A)

# variance of 2D array(axis=0, row-wise)
np.std(A2, axis=0)

# variance of 2D array(axis=1, column-wise)
np.std(A2, axis=0)

Compute the q-th quantile of the data along the specified axis.
- Syntax: np.quantile(array); array-wise quantile
- Syntax: np.quantile(array, axis=0); row-wise quantile
- Syntax: np.quantile(array, axis=1); column-wise quantile

# 25th percentile of `A`
np.quantile(A, 0.25)

# 50th percentile of `A2`(axis=0)
np.quantile(A2, 0.5, axis=0)

# 75th percentile of `A2`(axis=1)
np.quantile(A2, 0.75, axis=1)

# documentation 
np.info(np.corrcoef)

# compute Correlation Coefficient
np.corrcoef(A2)