The **mean squared error** (MSE) is largely used as a metric to determine the performance of an algorithm. 

The formula to calculate the MSE is as follows:

# Defining the variables 

1. $n$ - the total number of terms for which the error is to be calculated 
2. $y_i$ - the observed value of the variable
3. $\bar y_i$ - the predicted value of the variable

The mean square error is the average of the square of the difference between the observed and predicted values of a variable. 

In Python, the MSE can be calculated rather easily, especially with the use of lists.

# How to calculate MSE

1. Calculate the difference between each pair of the observed and predicted value
2. Take the square of the difference value
3. Add each of the squared differences to find the cumulative values
4. In order to obtain the average value, divide the cumulative value by the total number of items in the list 


# Example
Suppose you wish to calculate the MSE and are provided with the observed and predicted values. The steps mentioned above will be implemented as follows:

y = [11,20,19,17,10]
y_bar = [12,18,19.5,18,9]
summation = 0  #variable to store the summation of differences
n = len(y) #finding total number of items in list
for i in range (0,n):  #looping through each element of the list
  difference = y[i] - y_bar[i]  #finding the difference between observed and predicted value
  squared_difference = difference**2  #taking square of the differene 
  summation = summation + squared_difference  #taking a sum of all the differences
MSE = summation/n  #dividing summation by total values to obtain average
print "The Mean Square Error is: " , MSE

Calculating Mean Squared Error in Python

MSE measures algorithm performance by averaging squared differences between observed and predicted values, easily computable in Python using lists.