NumPy has np.percentile().

import numpy as np
a = np.array([1,2,3,4,5])
p = np.percentile(a, 50)  # return 50th percentile, i.e. median.

>>> print(p)
3.0

SciPy has scipy.stats.scoreatpercentile(), in addition to many other statistical goodies.

As mentioned in the comments count, min, and max are all built in so you can simply call count(your_list), max(your_list), min(your_list).

I would recommend using libraries such as Pandas, Numpy etc. if you can. If you are restricted only to the standard library you can also take a look at the statistics module.

For the others:

Mean

def mean(li):
    return sum(li) / len(li)

Standard Deviation

def std(li):
    mu = mean(li)
    return (sum((x-mu)**2 for x in li)/len(li)) ** 0.5

Quartiles

I will implement for any percentile, you can then use percentile(your_list, 25) or others as needed.

def percentile(li, percentile):
    n = len(li)
    idx = n * percentile / 100
    return sorted(li)[math.floor(idx)]

If you want to replicate Pandas describe function:

def describe(li):
   return f"""
   count    {len(li)}
   mean     {mean(li)}
   std      {std(li)}
   min      {min(li)}
   25%      {percentile(li, 25)}
   50%      {percentile(li, 50)}
   75%      {percentile(li, 75)}
   max      {max(li)}"""

By using pandas:

df.time_diff.quantile([0.25,0.5,0.75])


Out[793]: 
0.25    0.483333
0.50    0.500000
0.75    0.516667
Name: time_diff, dtype: float64