Question

Sample values from an experiment often need to be smoothed out. One approach is to replace each value with the mean of the previous n values, this is called the simple moving average. Implement a function, smooth (values, n ) that carries out this operation. The variable values is a list of numbers and n is the size of the moving average. The function should return a new list with the smoothed data. The new list should have n−1 fewer elements than the original list. For example, smooth ([3,5,1,5,6,8,9,10,15, 3], 3) should return [3.0,3.7,4.0,6.3,7.7,9.0,11.3,9.3].

Answer 1

The simple moving average smooths a sequence by replacing each number with the mean of the previous n numbers. A Python function 'smooth' can calculate this, resulting in a smoothed list of values with n-1 fewer elements than the original list.

Step-by-step explanation:

The simple moving average is a method used in statistics to create a smoothed sequence of numbers by replacing each number in a list with the average of the preceding n numbers. To implement a function smooth(values, n) that calculates this, you would iterate through the list of values. For each element from the n-th position to the end of the list, you calculate the mean of the 'window' consisting of the element itself and the n-1 previous elements. The resulting list of these means will be the smoothed data.

Here is an example of how the function would be implemented in Python:

def smooth(values, n):
smoothed_values = []
for i in range(n - 1, len(values)):
window = values[i-n+1:i+1]
window_average = sum(window) / n
smoothed_values.append(window_average)
return smoothed_values

For the given example, smooth([3,5,1,5,6,8,9,10,15,3], 3) would yield [3.0, 3.7, 4.0, 6.3, 7.7, 9.0, 11.3, 9.3].