Best way to graph & interpolate this dataset?

I am trying to figure out the best way to interpolate and graph this data. It represents the distribution of "likes" given by women to men on an online dating app:

hinge likes.PNG

So we could describe this as:

99-100th percentile = 16.4%
95-98.9th percentile = 24.7%
90-94.9th percentile = 16.9%
50-89.9th percentile = 37.7%
0-49.9th percentile = 4.3%

Dividing each group up per percentile equally looks roughly like this:

Distribution of Women's Likes of Men on Dating App Hinge.png

But of course this is not how the data would truly be shaped.

I haven't had any stats courses since first year of undergrad, so please talk simply to me if possible. :) But what would be the best way to graph this data to get a likely correct smoothed plot of it? Any programs/apps that can do it for free?