Get statistics (q1, median q3) from count dictionary

Question

I have a dictionary of counts like this:

{1:2, 2:1, 3:1}

I need to calculate q1, median, and q3 from this. It is pretty straight forward for odd numbered arrays but for even cases, I can't seem to figure it out. I want to do it without using any libraries like numpy.

Example:

counts = {
            "4": 1,
            "1": 2,
            "5": 1
        }

results = {
            "q1": 1,
            "median": 2.5,
            "q3": 4,
        }

I have something along these lines so far but this doesn't handle all cases.

def get_ratings_stats(counts):
    """"This function will return min, q1, median, q3 and max value from list of ratings."""

    cumulative_sum = 0
    cumulative_dict = {}
    for key, value in sorted(counts.items()):
        cumulative_sum += value
        cumulative_dict[key] = cumulative_sum

    q1_index = math.floor(cumulative_sum * 0.25)
    q3_index = math.ceil(cumulative_sum * 0.75)
    median_index = cumulative_sum * 0.5

    q1, q3, median = None, None, None
    print('indexes: ', q1_index, median_index, q3_index)
    for key, sum in cumulative_dict.items():
        if not q1 and sum >= q1_index:
            q1 = key
        if not q3 and sum >= q3_index:
            q3 = key
        if not median and sum >= median_index:
            median = key

Answer 1

OP's code is almost finished as it is, just problems with the final part. Different implementations are exposed and measured the different execution's times.

import math
import statistics as st # used for stats_with_stats & workbench


def stats_with_stats(data:dict):
    # flat the data
    f_table = []
    for v, freq in data.items():
        f_table.extend([v]*freq)
    return st.quantiles(f_table)


def stats_by_cards(data:dict):
    # no explicit extra container
    n = sum(data.values()) # total frequency

    q1_i = math.floor(n * 0.25)
    q2_i = n * 0.5
    q3_i = math.ceil(n * 0.75)

    qs = iter((q1_i, q2_i, q3_i))

    out_stats = []
    q = next(qs)
    cum_f = 0
    for v, freq in sorted(data.items()):
        cum_f_new = cum_f + freq
        if cum_f <= q < cum_f_new:
            out_stats.append(v)
            q = next(qs, None)
            if q is None:
                break
        cum_f = cum_f_new

    return out_stats


def stats_by_learner(data:dict):
    # using an extra container - it is more time consuming!
    tmp_data = {}
    f_cum = 0
    for v, f in sorted(data.items()):
        f_cum_new = f_cum + f
        tmp_data[v] = (f_cum, f_cum_new) # <- pairs
        f_cum = f_cum_new

    q1_i = math.floor(f_cum * 0.25)
    q2_i = f_cum * 0.5
    q3_i = math.ceil(f_cum * 0.75)

    qs = iter((q1_i, q2_i, q3_i))

    out_stats = []
    q = next(qs)
    for v, (lower_freq, upper_freq) in tmp_data.items():
        if lower_freq <= q < upper_freq:
            out_stats.append(v)
            q = next(qs, None)
            if q is None:
                break

    return out_stats        

Timing with the following dataset

from collections import Counter
import random

# test with sample dataset
random.seed(123456) # for sake of "reproducibility"
dataset = Counter([random.randint(1, 100) for _ in range(1_000)])

Output

dataset
length  1000
seed    123456

check outputs
stats_by_cards      [23, 49, 75]
stats_by_learner    [23, 49, 75]
stats_with_stats    [23.0, 49.0, 75.0]

timing:
quartiles with "stats_by_cards"
times           [28.688197855000908, 29.46196023000084, 27.1563763080012, 27.481716411999514, 27.487445683997066]
mean            28.055139297799904
std             0.9796393506117709
quartiles with "stats_by_learner"
times           [44.43848133800202, 37.32753902799959, 36.33182038599989, 36.39275053000165, 36.30151881200072]
mean            38.15842201880078
std             3.5366534480997154
quartiles with "stats_with_stats"
times           [79.48812012000053, 80.60817988300187, 81.6248098290016, 81.89885164600128, 81.02726684300069]
mean            80.9294456642012
std             0.950457690904102

Remark on the definition of quartiles: the way quartiles are implemented (as in OP) maybe not be consistent:

check outputs (with 50 terms & seed=123456)
stats_by_learner    [13, 42, 66]
stats_by_cards      [13, 42, 66]
stats_with_stats    [12.75, 40.5, 65.25]