a first shot at #44

Author: anthonyjpesce

calculate/pareto.py

@@ -1,6 +1,64 @@
-def pareto():
+def pareto(data_list):
     """
+    =IF (SUM (B$2:B8) > SUM(B$2:B$14)/2, (ABS( SUM(B$2:B$14)/2 - SUM(B$2:B7) ) / B8 ) * D8+C8,"")
+
     Estimate the mean using grouped data, like we get
-    from census age and income distributions
+    from census age and income distributions.
+
+    Takes a list of data, where each item contains a count of
+    the number of items that fall in that range, plus the
+    bottom end of the range and it's width.
+
+    Each item should look like this:
+        [COUNT, BOTTOM, TOP]
+
+    Here's a full example using age:
+
+    [   # count  # base  # width
+        [216350,    0,      5],     # Under 5 years
+        [201692,    5,      5],     # 5 to 9 years
+        [211151,    10,     5],     # 10 to 14 years
+        [204986,    15,     5],     # 15 to 19 years
+        [200257,    20,     5],     # 20 to 24 years
+        [439047,    25,     10],    # 25 to 34 years
+        [459664,    35,     10],    # 35 to 44 years
+        [424775,    45,     10],    # 45 to 54 years
+        [163492,    55,     5],     # 55 to 59 years
+        [127511,    60,     5],     # 60 to 64 years
+        [169552,    65,     10],    # 65 to 74 years
+        [113693,    75,     10],    # 75 to 84 years
+        [44661,     85,     10],    # 85 years and over
+    ]
+
     """
-    pass
+    counts = [float(i[0]) for i in data_list]
+    bases = [float(i[1]) for i in data_list]
+    widths = [float(i[2]) for i in data_list]
+
+    # break early if we don't have data
+    if not counts or sum(counts) == 0:
+        return 0
+
+    # Find the group that has the median in it
+    # Which will be the group at which the sum of the 
+    # cumulative counts is greater than the sum of all
+    # of the counts...
+    target = sum(counts) / 2
+    cumulative_counts = 0
+    index = 0
+    while cumulative_counts <= target:
+        cumulative_counts += counts[index]
+        index += 1
+
+    index -= 1
+    # Just to be verbose
+    median_group_count = counts[index]
+    median_group_base = bases[index]
+    median_group_width = widths[index]
+    # Calculate the sum of all of the groups prior to
+    # the one that contains the median 
+    previous_groups_sum = cumulative_counts - median_group_count
+
+    # Finally, calculate the median
+    median = median_group_base + ((sum(counts)/2 - previous_groups_sum)/median_group_count) * median_group_width
+    return median