This isn't the best way to do it. There are other ways to do this quickly. However, I do think this is a fairly straight forward and easy-to-understand example that was put together very hastily. I used this on your example and it works.
import csv
# replace "yourusername" with your PC user name
input_file = 'C:/Users/yourusername/Desktop/someFile.csv'
output_file = 'C:/Users/yourusername/Desktop/output.csv'
csv_file = open(input_file, newline='') # opening csv file
info = list(csv.reader(csv_file)) # convert data in csv file to array/list
csv_file.close()
length = len(info[0]) # if you ever add more headers, this will account for it
avg_container = [0 for i in range(length)] # creates empty array with zeros for each header
n = len(info[1:]) # for dividing by n to get average
# adding the lengths of all the items to one sum for each "column"
for k in info[1:]:
for n,i in enumerate(k):
avg_container[n] += len(i)
# diviving all sums by n
for i in range(len(avg_container)):
avg_container[i] = avg_container[i]/n
# combine header and average array into one item to write to csv
avg_output = []
avg_output.extend((info[0],avg_container))
print(avg_output) # just for you to see for yourself
# outputting the new file
output_csv = open(output_file, 'w', newline='') # creates an instance of the file
csv_writer = csv.writer(output_csv) # creates an "Writer" to write to the csv
csv_writer.writerows(avg_output) # outputs the avg_output variable to the csv file
output_csv.close() # finished
References
How to import a csv-file into a data array?
Create a .csv file with values from a Python list
Writing a Python list of lists to a csv file