Question

Python

An average is a number that shows a middle or normal value for a set of data. It is calculated by adding all the data points then dividing the total by the number of data points. A running average is an average that continually changes as more data points are collected.

In plain language, if there are n data points, we sum over those data points and divide by n. As soon as a new data point is collected, the number of data points now become n+1 and we again take the sum of these data points and divide by n+1. This turns out to be an inefficient way as we keep on summing over all the data points as soon as a new data point is added.

A more efficient way to calculate the new average is using the below formula:

new_average = (old_average*n + new_data_point)/(n+1)

Write the recursive function calc running average(), which takes three arguments: 1. data points: a list consisting of numbers (data points) collected over time. 2. data points till now: an integer which determines till what data point the current running average is being calculated for. This is the same as n in the above mentioned formula. 3. old average: a floating point number which determines the running average till the previous data point (i.e., for data points 0 through data points till now-1).

The function takes a list of data points, an index to keep track of which data points to consider and a variable to keep track of the old average.

The following rules apply: 1. For a list of data points of length n, there are n running averages. 2. After calculating average over some i data points and storing in the result list, you need to propagate this as the variable old average to calculate average over i+1 data points. 3. It is guaranteed that at there is at least 1 data point.

The function returns a list of floating point numbers, of same length as the list data points where the value at index i represents the running average over i+1 data points.

Remember: A list starts from index 0 but we count data points from index 1.

Clearly we need to use the same formula over and over again, each time incrementing the value of n and making the new average calculated as the old average for the next application of the formula.

Answer 1

First of all let me explain you the approach, as you know recursion works with some terminating condition ,so here we will terminate our recursion when we reach the last element.

see for example --

if we have the data_points as [1,2,3]

When we reach the last item 3 ,it will return a list containing average 2.0 (the average from beginning to that point) , then we come back to 2 from the recursion ,we shall append the average till 2 from the beginning (i.e 1.5) to the front of the list ,the new list becomes [1.5,2.0] , then again it comes back to 1 and here we append average till 1 from the beginning (i.e 1) to the front of the list ,the new list becomes [1,1.5,2.0].

Code --

def func(data_points,ind,old_av):
new_av=(old_av*ind+data_points[ind])/(ind+1)
if(ind==(len(data_points)-1)):
return [new_av]
else:
to_ret=func(data_points,ind+1,new_av)
to_ret=[new_av]+to_ret
return to_ret

The snippet is attached so you do not have any problem with indentation

Variables--

data_points--the list containing data points

ind--the current index to be processed(or we can say n i.e number of data points processed)

old_av-- the old average

new_av --the new average

to_ret-- the list that is to be returned

Code explanation--

line 1-- it is the function definition taking 3 parameters as mentioned data_points,ind,old_av

line 2--we calculate the new average using the formula given

line 3,4-- terminating condition ,if it is the last element return the list with single element containing average till last item

line 5,6,7-- if we have not reached the terminating condition we call the function on next data point ,here ind parameter is incremented to ind+1 and in place of old_av ,we pass new_av(because this will be the old average for the next data point) .Next we append the current running average to the front of the list returned (like we appended 1 to [1.5,2.0] in the explanation) and return this list.

note-- when calling the function , set data_points to your list ,ind=0 ,old_av=0

For example----

  func([1,2,3],0,0)