NumPy - Statistical Functions

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Statistical Functions in NumPy

NumPy offers a wide range of statistical functions that allow you to perform various statistical calculations on arrays. These functions can calculate metrics such as mean, median, variance, standard deviation, minimum, maximum, and more.

The NumPy amin() and amax() Functions

The numpy.amin() function returns the minimum from the elements in the given array along the specified axis. Whereas, the numpy.amax() function returns the maximum from the elements in the given array along the specified axis.

Example

In the following example, we are demonstrating how to use the amin() and amax() functions on a NumPy array −

import numpy as np 
a = np.array([[3,7,5],[8,4,3],[2,4,9]]) 

print('Our array is:') 
print(a)  
print('\n')  

print('Applying amin() function:') 
print(np.amin(a,1)) 
print('\n')  

print('Applying amin() function again:') 
print(np.amin(a,0)) 
print('\n')  

print('Applying amax() function:') 
print(np.amax(a)) 
print('\n')  

print('Applying amax() function again:') 
print(np.amax(a, axis=0))

It will produce the following output −

Our array is:
[[3 7 5]
 [8 4 3]
 [2 4 9]]
Applying amin() function:[3 3 2]
Applying amin() function again:[2 4 3]
Applying amax() function:9
Applying amax() function again:[8 7 9]

The numpy.ptp() Function

The numpy.ptp() function returns the range (maximum - minimum) of values along an axis.

Example

In the following example, we are using the ptp() function to calculate the range of values in a NumPy array −

import numpy as np 
a = np.array([[3,7,5],[8,4,3],[2,4,9]]) 

print('Our array is:') 
print(a) 
print('\n')  

print('Applying ptp() function:') 
print(np.ptp(a)) 
print('\n')  

print('Applying ptp() function along axis 1:') 
print(np.ptp(a, axis=1)) 
print('\n')   

print('Applying ptp() function along axis 0:')
print(np.ptp(a, axis=0)) 

Following is the output obtained −

Our array is:
[[3 7 5] 
 [8 4 3]
 [2 4 9]]
Applying ptp() function:7
Applying ptp() function along axis 1:[4 5 7]
Applying ptp() function along axis 0:[6 3 6]

The numpy.percentile() Function

Percentile (or a centile) is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall.

The numpy.percentile() function computes the q-th percentile of the data along the specified axis. It takes the following arguments −

numpy.percentile(a, q, axis)

Where,

• a: It is the input array.
• q: It is the percentile to compute and it must be between 0-100.
• axis: It is the axis along which the percentile is to be calculated.

Example

In this example, we are calculating the 50th percentile (median) of a NumPy array using the percentile() function −

import numpy as np 
a = np.array([[30,40,70],[80,20,10],[50,90,60]]) 

print('Our array is:') 
print(a) 
print('\n')  

print('Applying percentile() function:') 
print(np.percentile(a,50)) 
print('\n')  

print('Applying percentile() function along axis 1:') 
print(np.percentile(a,50, axis=1)) 
print('\n')  

print('Applying percentile() function along axis 0:') 
print(np.percentile(a,50, axis=0))

This will produce the following result −

Our array is:
[[30 40 70]
 [80 20 10]
 [50 90 60]]
Applying percentile() function:50.0
Applying percentile() function along axis 1:[40. 20. 60.]
Applying percentile() function along axis 0:[50. 40. 60.]

Sum and Product of Array Elements

The numpy.sum() function calculates the sum of all elements in the array, while the numpy.prod() function calculates the product of all elements in the array.

Example

In the following example, we are calculating the sum and product of the elements in a NumPy array using the sum() and prod() functions −

import numpy as np 

# Create a NumPy array
data = np.array([1, 2, 3, 4])

# Calculate the sum of the array
sum_value = np.sum(data)

# Calculate the product of the array
prod_value = np.prod(data)

print(f"Sum of the array: {sum_value}")
print(f"Product of the array: {prod_value}")

It will produce the following output −

Sum of the array: 10
Product of the array: 24

The numpy.median() Function

The numpy.median() function computes the median along the specified axis. If no axis is specified, it computes the median of the flattened array. Median is defined as the value separating the higher half of a data sample from the lower half

Example

In the following example, we are using the median() function to find the median of elements in a NumPy array −

import numpy as np 
a = np.array([[30,65,70],[80,95,10],[50,90,60]]) 

print('Our array is:') 
print(a) 
print('\n')  

print('Applying median() function:') 
print(np.median(a)) 
print('\n')  

print('Applying median() function along axis 0:') 
print(np.median(a, axis=0)) 
print('\n')  
 
print('Applying median() function along axis 1:') 
print(np.median(a, axis=1))

Following is the output of the above code −

Our array is:
[[30 65 70]
 [80 95 10]
 [50 90 60]]
Applying median() function:65.0
Applying median() function along axis 0:[50. 90. 60.]
Applying median() function along axis 1:[65. 80. 60.]

The numpy.mean() Function

The numpy.mean() function returns the arithmetic mean of elements in the array. If no axis is specified, it computes the mean of the flattened array. Arithmetic mean is the sum of elements along an axis divided by the number of elements.

Example

In the following example, we are calculating the mean of elements in a NumPy array using the mean() function −

import numpy as np 
a = np.array([[1,2,3],[3,4,5],[4,5,6]]) 

print('Our array is:') 
print(a) 
print('\n')  

print('Applying mean() function:') 
print(np.mean(a)) 
print('\n')  

print('Applying mean() function along axis 0:') 
print(np.mean(a, axis=0)) 
print('\n')  

print('Applying mean() function along axis 1:') 
print(np.mean(a, axis=1))

The output obtained is as shown below −

Our array is:
[[1 2 3]
 [3 4 5]
 [4 5 6]]
Applying mean() function:3.6666666666666665
Applying mean() function along axis 0:[2.66666667 3.66666667 4.66666667]
Applying mean() function along axis 1:[2. 4. 5.]

The numpy.average() Function

The numpy.average() function computes the weighted average of elements in an array according to their respective weight. Weighted average is an average resulting from the multiplication of each component by a factor.

Example

In the example below, we are calculating the average of elements in a NumPy array using the average() function with and without weights −

import numpy as np 
a = np.array([1,2,3,4]) 

print('Our array is:') 
print(a) 
print('\n')  

print('Applying average() function without weights:') 
print(np.average(a)) 
print('\n')  

wts = np.array([4,3,2,1]) 

print('Applying average() function with weights:') 
print(np.average(a,weights=wts)) 
print('\n')  

print('Sum of weights') 
print(np.average([1,2,3,4],weights=[4,3,2,1], returned=True)) 

It will produce the following output −

Our array is:[1 2 3 4]
Applying average() function without weights:2.5
Applying average() function with weights:2.0
Sum of weights(2.0, 10.0)

The numpy.std() Function

The numpy.std() function returns the standard deviation of elements in the array. The standard deviation is the square root of the average of squared deviations from the mean, i.e., std = sqrt(mean(abs(x - x.mean())**2)).

Example

In the following example, we are using the std() function to calculate the standard deviation of a NumPy array −

import numpy as np 
print(np.std([1,2,3,4])) 

After executing the above code, we get the following output −

1.118033988749895

The numpy.var() Function

The numpy.var() function returns the variance of elements in the array. The variance is the average of squared deviations, i.e., var = mean(abs(x - x.mean())**2).

Example

In the following example, we are using the var() function to calculate the variance of a NumPy array −

import numpy as np 
print(np.var([1,2,3,4]))

We get the output as shown below −

1.25

Correlation Coefficient

The numpy.corrcoef() function returns the Pearson correlation coefficients of the input array. It is useful for determining the relationship between two variables.

Example

In the following example, we are calculating the correlation coefficient matrix for two arrays using the corrcoef() function −

import numpy as np 

# Define two arrays
data1 = np.array([1, 2, 3, 4, 5])
data2 = np.array([5, 4, 3, 2, 1])

# Calculate the correlation coefficient
corr_coef = np.corrcoef(data1, data2)

print("Correlation Coefficient Matrix:")
print(corr_coef)

The result is as shown below −

Correlation Coefficient Matrix:
[[ 1. -1.]
 [-1.  1.]]

Statistical Funtions

Following are the different Statistical function in Numpy −

Sr.No.	Functions & Description
1	amin() Return the minimum of an array or minimum along an axis
2	amax() Return the maximum of an array or maximum along an axis
3	nanmin() Return minimum of an array or minimum along an axis, ignoring any NaNs
4	nanmax() Return the maximum of an array or maximum along an axis, ignoring any NaNs
5	ptp() Range of values (maximum - minimum) along an axis
6	percentile() Compute the q-th percentile of the data along the specified axis
7	nanpercentile() Compute the qth percentile of the data along the specified axis, while ignoring nan values
8	quantile() Compute the q-th quantile of the data along the specified axis
9	nanquantile() Compute the qth quantile of the data along the specified axis, while ignoring nan values. Returns the qth quantile(s) of the array elements
10	median() Compute the median along the specified axis
11	average() Compute the weighted average along the specified axis
12	mean() Compute the arithmetic mean along the specified axis
13	std() Compute the standard deviation along the specified axis
14	var() Compute the variance along the specified axis
15	nanmean() Compute the arithmetic mean along the specified axis, ignoring NaNs
16	nanstd() Compute the standard deviation along the specified axis, while ignoring NaNs
17	nanvar() Compute the variance along the specified axis, while ignoring NaNs