If you want to find the x-value that corresponds to p% of all comments, simply sort the list of values and then locate it at the p% position based on the total length. Adding vertical lines at these positions and including a second x-axis with labels can help visually represent this data.
To determine the x-value for p% of all tokens, identify where the element with a value of p% of the sum of all the x's is situated in the array containing the cumulative sum of the sorted list. This position can be used to index the sorted list of values.
Below is an example code snippet illustrating how this concept could be implemented:
from matplotlib import pyplot as plt
import numpy as np
# Generate random data for testing purposes, convert to a standard Python list for consistency with the original question
x = list(np.abs(np.random.normal(85, 30, 2000)))
wanted_percentiles = [5, 10, 25, 33, 50, 66, 75, 90, 95]
sx = np.array(x)
sx.sort()
cx = sx.cumsum()
percentile_sx = [sx[int(len(x) * p / 100)] for p in wanted_percentiles]
percentile_cx = [sx[cx.searchsorted(cx[-1] * p / 100)] for p in wanted_percentiles]
fig, axes = plt.subplots(ncols=2, figsize=(12, 4))
for ax, percentile, color, title in zip(axes, [percentile_sx, percentile_cx],
['crimson', 'limegreen'], ['Comments Percentile', 'Tokens Percentile']):
ax.hist(x, bins=20)
for xp in percentile:
ax.axvline(xp, color=color)
ax2 = ax.twiny()
ax.set_xlim(0, 150)
ax2.set_xlim(ax.get_xlim()) # ensure both axes have identical limits
ax2.set_xticks(percentile) # assign xs corresponding to percentiles as tick positions
ax2.set_xticklabels(wanted_percentiles, color=color) # use percentiles for labeling ticks
ax.set_title("Distribution of Comment Lengths, " + title)
ax.set_xlabel("Comments binned by number of tokens")
ax.set_ylabel("Number of Comments")
plt.show()
The plot on the left showcases data with 100 bins, while the one on the right demonstrates how it would appear with 20 bins:
https://i.stack.imgur.com/W2qth.png