As pointed out above, it gives "Down" arbitrarily, but not randomly. On the same machine with the same Pandas version, running the above code should always yield the same result (although it's not guaranteed by the docs, see comments below).

Let's reproduce what's happening.

Given this series:

abc = pd.Series(list("abcdefghijklmnoppqq"))

The value_counts implementation boils down to this:

import pandas._libs.hashtable as htable
keys, counts = htable.value_count_object(np.asarray(abc), True)
result = pd.Series(counts, index=keys)

result:

g    1
e    1
f    1
h    1
o    1
d    1
b    1
q    2
j    1
k    1
i    1
p    2
n    1
l    1
c    1
m    1
a    1
dtype: int64

The order of the result is given by the implementation of the hash table. It is the same for every call.

You could look into the implementation of value_count_object, which calls build_count_table_object, which uses the khash implementation to get more details about the hashing.

After computing the table, the value_counts implementation is sorting the results with quicksort. This sort is not stable and with this specially constructed example reorders "p" and "q":

result.sort_values(ascending=False)

q    2
p    2
a    1
e    1
f    1
h    1
o    1
d    1
b    1
j    1
m    1
k    1
i    1
n    1
l    1
c    1
g    1
dtype: int64

Thus there are potentially two factors for the ordering: first the hashing, and second the non-stable sort.

The displayed top value is then just the first entry of the sorted list, in this case, "q".

On my machine, quicksort becomes non-stable at 17 entries, this is why I chose the example above.

We can test the non-stable sort with this direct comparison:

pd.Series(list("abcdefghijklmnoppqq")).describe().top
'q'

pd.Series(list(               "ppqq")).describe().top
'p'

As with any series, you can access a value by label via the dot notation or the square brackets __getitem__ notation.

In this case, it's simply df.describe().top or df.describe()['top'].

As of pandas v15.0, use the parameter, DataFrame.describe(include = 'all') to get a summary of all the columns when the dataframe has mixed column types. The default behavior is to only provide a summary for the numerical columns.

Example:

In[1]:

df = pd.DataFrame({'$a':['a', 'b', 'c', 'd', 'a'], '$b': np.arange(5)})
df.describe(include = 'all')

Out[1]:

        $a    $b
count   5   5.000000
unique  4   NaN
top     a   NaN
freq    2   NaN
mean    NaN 2.000000
std     NaN 1.581139
min     NaN 0.000000
25%     NaN 1.000000
50%     NaN 2.000000
75%     NaN 3.000000
max     NaN 4.000000

The numerical columns will have NaNs for summary statistics pertaining to objects (strings) and vice versa.

Summarizing only numerical or object columns

1. To call describe() on just the numerical columns use describe(include = [np.number])

2. To call describe() on just the objects (strings) using describe(include = ['O']).

   In[2]:
   
   df.describe(include = [np.number])
   
   Out[3]:
   
            $b
   count   5.000000
   mean    2.000000
   std     1.581139
   min     0.000000
   25%     1.000000
   50%     2.000000
   75%     3.000000
   max     4.000000
   
   In[3]:
   
   df.describe(include = ['O'])
   
   Out[3]:
   
       $a
   count   5
   unique  4
   top     a
   freq    2
   

what is the purpose of top function in output, and how it will work?

If you execute:

df.Name.value_counts()

You will see the value of a person in the Name column and their counts. top gives the highest counted value of the categorical values.

Example:

d ={'Name':pd.Series(['Tom','Steve','Ricky','Vin','Steve','Smith','Jack',
'Lee','David','Gasper','Betina','Andres']),
'Age':pd.Series([25,26,25,23,30,29,23,34,40,30,51,46]),   
'Rating':pd.Series([4.23,3.24,3.98,2.56,3.20,4.6,3.8,3.78,
2.98,4.80,4.10, 
3.65])
}
#Create a DataFrame
df = pd.DataFrame(d)
print(df.describe(include='all'))

        Name        Age     Rating
count      12  12.000000  12.000000
unique     11        NaN        NaN
top     Steve        NaN        NaN
freq        2        NaN        NaN
mean      NaN  31.833333   3.743333
std       NaN   9.232682   0.661628
min       NaN  23.000000   2.560000
25%       NaN  25.000000   3.230000
50%       NaN  29.500000   3.790000
75%       NaN  35.500000   4.132500
max       NaN  51.000000   4.800000

print(df.Name.value_counts())

Steve     2
Ricky     1
Tom       1
Andres    1
Jack      1
Smith     1
Lee       1
Betina    1
Vin       1
Gasper    1
David     1

Since Name count for Steve is highest, it comes in top.