# Mathematics and Programming for FinTech

1) The median, mode, and mean are basic statistical functions for data analytics. In this question, you will implement them in pure Python code without importing any packages.

The following notations are used:

• v is a non-empty “list of numbers”
• vm is a non-empty “list of numbers” OR “list of non-empty lists of numbers” where the sub-lists have equal lengths.

a) Create a function median(v) which returns the median of v
b) Create a function mode (v) that returns a list containing the modes of v. Note that it is possible to have more than one mode, hence we return a list.
c) Create a function mean(vm, axis=None) which returns the mean of vm. The return value depends on the value of the axis as follows:

• 0: returns the mean down the rows
• 1: returns the mean across the columns
• None: return the mean of all the entries in vm

d) Show the result of your code running against these test cases:

• median(v), modes(v) and mean(v) for

v = [i for j in (range(1180, 2022, k)
for k in (3, 5, 7)) for i in j]

• mean(vm), mean(vm, 0) and mean(vm, 1) for

vm = [[11, 12, 13, 14, 15, 16, 17, 18],
[21, 22, 23, 24, 25, 26, 27, 28],

[91, 92, 93, 94, 95, 96, 97, 98]]