Implementing Spread in Python
Define the Dataset
Here, we assign an array to the variable data to ensure we have a consistent dataset to work with for all calculations.
import numpy as np
# Create a numpy array of daily sales
data = np.array([10, 15, 12, 18, 20, 22, 14, 17, 11, 16])
Calculate Population Statistics
This function takes the array as input and returns the average value of all elements, which summarizes the central tendency of the dataset.
mean_val = np.mean(data) # Mean
variance_val = np.var(data) # Population variance (ddof=0 by default)
std_dev_val = np.std(data) # Population standard deviation
np.mean(data)computes the arithmetic mean (average);np.var(data)calculates the population variance (divides by n);np.std(data)calculates the population standard deviation (square root of variance).
123456789101112import numpy as np # Create a numpy array of daily sales data = np.array([10, 15, 12, 18, 20, 22, 14, 17, 11, 16]) mean_val = np.mean(data) # Mean variance_val = np.var(data) # Population variance (ddof=0 by default) std_dev_val = np.std(data) # Population standard deviation print(f"Mean: {mean_val}") print(f"Variance (Population): {variance_val}") print(f"Standard Deviation (Population): {std_dev_val}")
Calculate Sample Statistics
To get unbiased estimates from a sample, we use ddof=1.
This applies Bessel's correction, dividing variance by $(n-1)$ instead of $n$.
sample_variance_val = np.var(data, ddof=1)
sample_std_dev_val = np.std(data, ddof=1)
np.var(data, ddof=1)- sample variance;np.std(data, ddof=1)- sample standard deviation.
12345678910import numpy as np # Create a numpy array of daily sales data = np.array([10, 15, 12, 18, 20, 22, 14, 17, 11, 16]) sample_variance_val = np.var(data, ddof=1) sample_std_dev_val = np.std(data, ddof=1) print(f"Variance (Sample): {sample_variance_val}") print(f"Standard Deviation (Sample): {sample_std_dev_val}")
Standard deviation is the square root of variance, giving a measure of spread in the same units as the original data, making it easier to interpret.
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Define the Dataset
Here, we assign an array to the variable data to ensure we have a consistent dataset to work with for all calculations.
import numpy as np
# Create a numpy array of daily sales
data = np.array([10, 15, 12, 18, 20, 22, 14, 17, 11, 16])
Calculate Population Statistics
This function takes the array as input and returns the average value of all elements, which summarizes the central tendency of the dataset.
mean_val = np.mean(data) # Mean
variance_val = np.var(data) # Population variance (ddof=0 by default)
std_dev_val = np.std(data) # Population standard deviation
np.mean(data)computes the arithmetic mean (average);np.var(data)calculates the population variance (divides by n);np.std(data)calculates the population standard deviation (square root of variance).
123456789101112import numpy as np # Create a numpy array of daily sales data = np.array([10, 15, 12, 18, 20, 22, 14, 17, 11, 16]) mean_val = np.mean(data) # Mean variance_val = np.var(data) # Population variance (ddof=0 by default) std_dev_val = np.std(data) # Population standard deviation print(f"Mean: {mean_val}") print(f"Variance (Population): {variance_val}") print(f"Standard Deviation (Population): {std_dev_val}")
Calculate Sample Statistics
To get unbiased estimates from a sample, we use ddof=1.
This applies Bessel's correction, dividing variance by $(n-1)$ instead of $n$.
sample_variance_val = np.var(data, ddof=1)
sample_std_dev_val = np.std(data, ddof=1)
np.var(data, ddof=1)- sample variance;np.std(data, ddof=1)- sample standard deviation.
12345678910import numpy as np # Create a numpy array of daily sales data = np.array([10, 15, 12, 18, 20, 22, 14, 17, 11, 16]) sample_variance_val = np.var(data, ddof=1) sample_std_dev_val = np.std(data, ddof=1) print(f"Variance (Sample): {sample_variance_val}") print(f"Standard Deviation (Sample): {sample_std_dev_val}")
Standard deviation is the square root of variance, giving a measure of spread in the same units as the original data, making it easier to interpret.
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