Course Content

Ultimate NumPy

Statistical Operations

Performing various statistical operations on arrays is essential for data analysis and machine learning. NumPy provides functions and methods to perform them effectively.

Measures of Central Tendency

Measures of central tendency represent a central or representative value within a probability distribution. Most of the time, however, you will calculate these measures for a certain sample.

Here are the two main measures:

Mean: the sum of all values divided by the total number of values;
Median: The middle value in a sorted sample.

NumPy provides mean() and median() functions for calculating the mean and median, respectively:


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import numpy as np
sample = np.array([10, 25, 15, 30, 20, 10, 2])
# Calculating the mean
sample_mean = np.mean(sample)
print(f'Sorted sample: {np.sort(sample)}')
# Calculating the median
sample_median = np.median(sample)
print(f'Mean: {sample_mean}, median: {sample_median}')

We also displayed the sorted sample so you can clearly see the median. Our sample has an odd number of elements (7), so the median is simply the element at index (n + 1) / 2 in the sorted sample, where n is the size of the sample.

Note

When the sample has an even number of elements, the median is the average of the elements at index n / 2 and n / 2 - 1 in the sorted sample.


              1234
            
import numpy as np
sample = np.array([1, 2, 8, 10, 15, 20, 25, 30])
sample_median = np.median(sample)
print(f'Median: {sample_median}')

Our sample is already sorted and has 8 elements, so n / 2 - 1 = 3 and sample[3] is 10. n / 2 = 4 and sample[4] is 15. Therefore, our median is (10 + 15) / 2 = 12.5.

Measures of Spread

Two measures of spread are variance and standard deviation. Variance measures how spread out the data is. It is equal to the average of the squared differences of each value from the mean.

Standard deviation is the square root of the variance. It provides a measure of how spread out the data is in the same units as the data.

NumPy has the var() function to calculate the variance of the sample and the std() function to calculate the standard deviation of the sample:


              1234567
            
import numpy as np
sample = np.array([10, 25, 15, 30, 20, 10, 2])
# Calculating the variance
sample_variance = np.var(sample)
# Calculating the standard deviation
sample_std = np.std(sample)
print(f'Variance: {sample_variance}, standard deviation: {sample_std}')

Calculations in Higher Dimensional Arrays

All of these functions have a second parameter axis. Its default value is None, which means that the measure will be calculated along a flattened array (even if the original array is 2D or higher dimensional).

You can also specify the exact axis along which to calculate the measure:


              12345678
            
import numpy as np
array_2d = np.array([[1, 2, 3], [4, 5, 6]])
# Calculating the mean in a flattened array
print(np.mean(array_2d))
# Calculating the mean along axis 0
print(np.mean(array_2d, axis=0))
# Calculating the mean along axis 1
print(np.mean(array_2d, axis=1))

The picture below shows the structure of the exam_scores array used in the task:

Task

Swipe to show code editor

You are analyzing the exam_scores array, a 2D array of simulated test scores for 5 students (5 columns) across 2 different exams (2 rows).

Calculate the mean score for each exam by specifying the second keyword argument.
Calculate the median of all scores.
Calculate the variance of all scores.
Calculate the standard deviation of all scores.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

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Thanks for your feedback!

Section 4. Chapter 3

Statistical Operations

Performing various statistical operations on arrays is essential for data analysis and machine learning. NumPy provides functions and methods to perform them effectively.

Measures of Central Tendency

Measures of central tendency represent a central or representative value within a probability distribution. Most of the time, however, you will calculate these measures for a certain sample.

Here are the two main measures:

Mean: the sum of all values divided by the total number of values;
Median: The middle value in a sorted sample.

NumPy provides mean() and median() functions for calculating the mean and median, respectively:


              12345678
            
import numpy as np
sample = np.array([10, 25, 15, 30, 20, 10, 2])
# Calculating the mean
sample_mean = np.mean(sample)
print(f'Sorted sample: {np.sort(sample)}')
# Calculating the median
sample_median = np.median(sample)
print(f'Mean: {sample_mean}, median: {sample_median}')

Note

When the sample has an even number of elements, the median is the average of the elements at index n / 2 and n / 2 - 1 in the sorted sample.


              1234
            
import numpy as np
sample = np.array([1, 2, 8, 10, 15, 20, 25, 30])
sample_median = np.median(sample)
print(f'Median: {sample_median}')

Our sample is already sorted and has 8 elements, so n / 2 - 1 = 3 and sample[3] is 10. n / 2 = 4 and sample[4] is 15. Therefore, our median is (10 + 15) / 2 = 12.5.

Measures of Spread

Two measures of spread are variance and standard deviation. Variance measures how spread out the data is. It is equal to the average of the squared differences of each value from the mean.

Standard deviation is the square root of the variance. It provides a measure of how spread out the data is in the same units as the data.

NumPy has the var() function to calculate the variance of the sample and the std() function to calculate the standard deviation of the sample:


              1234567
            
import numpy as np
sample = np.array([10, 25, 15, 30, 20, 10, 2])
# Calculating the variance
sample_variance = np.var(sample)
# Calculating the standard deviation
sample_std = np.std(sample)
print(f'Variance: {sample_variance}, standard deviation: {sample_std}')

Calculations in Higher Dimensional Arrays

You can also specify the exact axis along which to calculate the measure:


              12345678
            
import numpy as np
array_2d = np.array([[1, 2, 3], [4, 5, 6]])
# Calculating the mean in a flattened array
print(np.mean(array_2d))
# Calculating the mean along axis 0
print(np.mean(array_2d, axis=0))
# Calculating the mean along axis 1
print(np.mean(array_2d, axis=1))

The picture below shows the structure of the exam_scores array used in the task:

Task

Swipe to show code editor

You are analyzing the exam_scores array, a 2D array of simulated test scores for 5 students (5 columns) across 2 different exams (2 rows).

Calculate the mean score for each exam by specifying the second keyword argument.
Calculate the median of all scores.
Calculate the variance of all scores.
Calculate the standard deviation of all scores.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Thanks for your feedback!

Section 4. Chapter 3

Switch to desktop for real-world practiceContinue from where you are using one of the options below