Added statistics helpers

GeorgeSeif · GeorgeSeif · commit a6dc955960d0 · 2017-09-28T18:20:54.000-04:00
diff --git a/README.md b/README.md
@@ -23,7 +23,8 @@ To install all of the libraries, run the commands in the "install.txt" file. The
 
 ## Files
 - **ml_helpers.py:** Machine Learning helper functions. Adapted from my [Python Machine Learning](https://github.com/GeorgeSeif/Python-Machine-Learning) repository
-- **plt_helpers:** Helper functions to make plotting easy in Matplotlib.
+- **plt_helpers.py:** Helper functions to make plotting easy in Matplotlib.
+- **statistics_helpers.py:** Helper functions for computing dataset statistics
 - **explore_wine_data.py:** Exploratory data analysis of the wine dataset from sklearn using visualisations. Includes data analysis using histogram, scatterplot, bee swarm plot, and cumulative distribution function.
 - **statistics_iris.py:** Compute various statistics of the iris dataset features such as histogram, min, max, median, mean, and variance.
 - **covariance_boston.py:** Compute the covariance matrix of the Boston Housing dataset. These matrices can sometimes give faster insight into which variables are related rather than creating scatter plots.
diff --git a/statistics_helpers.py b/statistics_helpers.py
@@ -0,0 +1,60 @@
+import math
+
+def mean(x): 
+    return sum(x) / len(x)
+
+def median(v):
+    """finds the 'middle-most' value of v"""
+    n = len(v)
+    sorted_v = sorted(v)
+    midpoint = n // 2
+    
+    if n % 2 == 1:
+        # if odd, return the middle value
+        return sorted_v[midpoint]
+    else:
+        # if even, return the average of the middle values
+        lo = midpoint - 1
+        hi = midpoint
+        return (sorted_v[lo] + sorted_v[hi]) / 2
+        
+def quantile(x, p):
+    """returns the pth-percentile value in x"""
+    p_index = int(p * len(x))
+    return sorted(x)[p_index]
+
+def mode(x):
+    """returns a list, might be more than one mode"""
+    counts = Counter(x)
+    max_count = max(counts.values())
+    return [x_i for x_i, count in counts.iteritems()
+            if count == max_count]
+
+
+def data_range(x):
+    return max(x) - min(x)
+
+def variance(x):
+    """assumes x has at least two elements"""
+    n = len(x)
+    deviations = de_mean(x)
+    return sum_of_squares(deviations) / (n - 1)
+    
+def standard_deviation(x):
+    return math.sqrt(variance(x))
+
+def interquartile_range(x):
+    return quantile(x, 0.75) - quantile(x, 0.25)
+
+
+def covariance(x, y):
+    n = len(x)
+    return dot(de_mean(x), de_mean(y)) / (n - 1)
+
+def correlation(x, y):
+    stdev_x = standard_deviation(x)
+    stdev_y = standard_deviation(y)
+    if stdev_x > 0 and stdev_y > 0:
+        return covariance(x, y) / stdev_x / stdev_y
+    else:
+        return 0 # if no variation, correlation is zero
