Cheatsheets
Learn Statistics with NumPy

Learn Statistics with NumPy

Getting Started with NumPy

How to Filter NumPy Arrays

You can filter elements in a NumPy array based on a condition. For example, you can get all positive numbers from an array using a condition.

                                

import numpy as np
numbers = np.array([-5, 4, 0, 2, 3])
positives = numbers[numbers > 0]
print(positives)
# Output: [4, 2, 3]

Using Conditions with NumPy Arrays

NumPy allows you to perform logical operations on arrays. For example, you can create an array of True or False values based on a condition applied to another array.

                                

import numpy as np
numbers = np.array([-5, 4, 0, 2, 3])
is_positive = numbers > 0
print(is_positive)
# Output: [False, True, False, True, True]

Loading Data into NumPy Arrays

You can create NumPy arrays from data in files, like CSV files, using the `np.genfromtxt()` function.

                                

  import numpy as np
  data = np.genfromtxt('data.csv', delimiter=',')  # Correct for CSV
  print(data)

Creating NumPy Arrays from Lists

NumPy arrays can be created from lists or other iterable data structures using `np.array()`.

                                

import numpy as np
my_array = np.array([1, 2, 3, 4])
print(my_array)
# Output: [1 2 3 4]

Accessing Elements in a NumPy Array

You can access specific elements in a NumPy array by specifying their indices. For example, `array[0, 0]` accesses the first element of a 2D array.

                                

import numpy as np
matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print(matrix[0, 0]) 
# Output: 1
print(matrix[1, :])
# Output: [4, 5, 6]

Performing Arithmetic with NumPy Arrays

NumPy allows you to perform arithmetic operations on arrays element-wise. For example, adding two arrays together adds corresponding elements.

                                

import numpy as np
odds = np.array([1, 3, 5, 7, 9])
evens = odds + 1
print(evens)
# Output: [2, 4, 6, 8, 10]
array1 = np.array([1, 2, 3])
array2 = np.array([4, 3, 2])
new_array = array1 + array2
print(new_array)
# Output: [5, 5, 5]

Using NumPy for Statistics

Plotting Data Distributions

Histograms are used to visualize the distribution of data. They show how frequently each range of values occurs in a dataset.

                                

import numpy as np
import matplotlib.pyplot as plt
mu = 0 # mean
sigma = 0.1 # standard deviation
data = np.random.normal(mu, sigma, 1000)
plt.hist(data, bins=30)
plt.show()

Creating a Normal Distribution

A normal distribution is a common way to describe data that clusters around a mean value. You can visualize it using histograms.

                                

import numpy as np
import matplotlib.pyplot as plt
mu = 0 # mean
sigma = 1 # standard deviation
data = np.random.normal(mu, sigma, 1000)
plt.hist(data, bins=30)
plt.show()

Calculating Standard Deviation

The standard deviation measures how spread out the numbers in a dataset are from the mean. A higher standard deviation means more spread.

                                

import numpy as np
ring_toss = np.array([[1, 0, 0], [0, 0, 1], [1, 0, 1]])
avg_per_row = np.mean(ring_toss, axis=1)
print(avg_per_row)
# Output: [0.33333333 0.33333333 0.66666667]

Visualizing Histograms

Histograms help you see the spread and frequency of data points. For example, you can see how many times data points fall into certain ranges.

                                

import numpy as np
import matplotlib.pyplot as plt
data = np.array([1, 2, 3, 4, 4, 4, 6, 6, 7, 8, 8])
plt.hist(data, bins=10, color='blue')
plt.show()

Understanding Percentiles

Percentiles tell you the value below which a given percentage of observations fall. For example, the 50th percentile is the median.

                                

import numpy as np
data = np.array([1, 2, 3, 4, 4, 4, 6, 6, 7, 8, 8])
percentile_25 = np.percentile(data, 25)
percentile_75 = np.percentile(data, 75)
print(percentile_25)
# Output: 3.5
print(percentile_75)
# Output: 6.5

Calculating Mean with NumPy

The mean is the average of all numbers in a dataset. NumPy provides a function to calculate the mean easily.

                                

import numpy as np
heights = np.array([49.7, 46.9, 62, 47.2, 47, 48.3, 48.7])
mean_height = np.mean(heights)
print(mean_height)
# Output: 48.6

Sorting Data with NumPy

NumPy provides functions to sort arrays. Sorting helps in organizing data and finding patterns.

                                

import numpy as np
heights = np.array([49.7, 46.9, 62, 47.2, 47, 48.3, 48.7])
sorted_heights = np.sort(heights)
print(sorted_heights)
# Output: [46.9 47.  47.2 48.3 48.7 49.7 62. ]

Understanding Data Spread

68% of the data in a normal distribution will fall within one standard deviation of the mean. This shows where most data points are clustered around the mean.

More Data Spread Information

95% of data in a normal distribution will fall within two standard deviations of the mean, showing a wider range of data points.

Extreme Data Spread

99.7% of data in a normal distribution will fall within three standard deviations of the mean, covering almost all data points.

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