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Absolute Deviation and Absolute Mean Deviation using NumPy

Absolute deviation is a measure of variability that captures the distance between each observation in a dataset and the central point of that dataset. The absolute mean deviation (AMD) is the average of these absolute deviations.

Here's a tutorial on how to calculate both absolute deviation and absolute mean deviation using NumPy:

1. Absolute Deviation

The absolute deviation of an observation from its central point is simply the absolute value of the difference between the observation and the central point.

Formula: ADi=∣xi−m∣

Where:

xi = each observation in the dataset
m = the central point (usually the mean or median)

Let's implement this using Python and NumPy:

import numpy as np

# Sample data
data = np.array([2, 4, 4, 4, 5, 5, 7, 9])

# Calculate mean
mean_data = np.mean(data)

# Calculate absolute deviation
absolute_deviation = np.abs(data - mean_data)
print(absolute_deviation)

2. Absolute Mean Deviation

To get the absolute mean deviation, you simply take the average of all the absolute deviations.

Formula: AMD=n1∑i=1n∣xi−m∣

Where:

n = number of observations
xi = each observation in the dataset
m = the central point (usually the mean or median)

Let's compute the AMD using Python and NumPy:

# Calculate absolute mean deviation
absolute_mean_deviation = np.mean(absolute_deviation)
print(absolute_mean_deviation)

Putting it all together:

import numpy as np

# Sample data
data = np.array([2, 4, 4, 4, 5, 5, 7, 9])

# Calculate mean
mean_data = np.mean(data)

# Calculate absolute deviation
absolute_deviation = np.abs(data - mean_data)

# Calculate absolute mean deviation
absolute_mean_deviation = np.mean(absolute_deviation)

print("Absolute Deviation:", absolute_deviation)
print("Absolute Mean Deviation:", absolute_mean_deviation)

That's it! With just a few lines of code using NumPy, you can easily compute the absolute deviation and absolute mean deviation of a dataset.

1. Absolute Deviation NumPy:

Absolute deviation measures how much individual elements of a dataset deviate from the mean.

import numpy as np

data = np.array([2, 4, 4, 4, 5, 5, 7, 9])

mean = np.mean(data)
absolute_deviation = np.abs(data - mean)

print("Absolute Deviation:", absolute_deviation)

2. Absolute Mean Deviation in NumPy:

Absolute Mean Deviation is the average of absolute deviations.

import numpy as np

data = np.array([2, 4, 4, 4, 5, 5, 7, 9])

mean = np.mean(data)
absolute_deviation = np.abs(data - mean)
absolute_mean_deviation = np.mean(absolute_deviation)

print("Absolute Mean Deviation:", absolute_mean_deviation)

3. NumPy absolute deviation example:

An example showing how to calculate the absolute deviation using NumPy.

import numpy as np

data = np.array([10, 12, 15, 17, 20])

mean = np.mean(data)
absolute_deviation = np.abs(data - mean)

print("Data:", data)
print("Absolute Deviation:", absolute_deviation)

4. Calculate absolute deviation using NumPy:

Calculating the absolute deviation using NumPy's absolute function.

import numpy as np

data = np.array([3, 5, 8, 10, 12])

absolute_deviation = np.absolute(data - np.mean(data))

print("Absolute Deviation:", absolute_deviation)

5. Python NumPy MAD (Mean Absolute Deviation):

Using NumPy to calculate the MAD (Mean Absolute Deviation).

import numpy as np

data = np.array([3, 5, 8, 10, 12])

mad = np.mean(np.absolute(data - np.mean(data)))

print("Mean Absolute Deviation (MAD):", mad)

6. NumPy absolute deviation formula:

Understanding the formula for calculating absolute deviation in NumPy.

import numpy as np

data = np.array([3, 5, 8, 10, 12])

mean = np.mean(data)
absolute_deviation = np.abs(data - mean)

print("Absolute Deviation Formula:", absolute_deviation)

7. NumPy absolute deviation function:

Using NumPy's built-in function for calculating absolute deviation.

import numpy as np

data = np.array([3, 5, 8, 10, 12])

absolute_deviation = np.abs(np.subtract(data, np.mean(data)))

print("Absolute Deviation (Using NumPy function):", absolute_deviation)

8. Absolute deviation and mean absolute deviation with NumPy:

Calculating both absolute deviation and mean absolute deviation using NumPy.

import numpy as np

data = np.array([3, 5, 8, 10, 12])

mean = np.mean(data)
absolute_deviation = np.abs(data - mean)
mean_absolute_deviation = np.mean(absolute_deviation)

print("Absolute Deviation:", absolute_deviation)
print("Mean Absolute Deviation:", mean_absolute_deviation)

9. NumPy absolute difference array:

Using NumPy to create an array of absolute differences.

import numpy as np

array1 = np.array([2, 5, 8, 12])
array2 = np.array([3, 7, 8, 10])

absolute_difference = np.abs(array1 - array2)

print("Array 1:", array1)
print("Array 2:", array2)
print("Absolute Difference Array:", absolute_difference)