Parameter Estimation

Parameter: Summarized Population metric. Example mean, mode, median etc. for the population

Estimating parameter: Predicting / Coming up with a summarized value using your sample data for the population

 

For example: We have a sample of weights of 100 people and we want to find the average weight of the whole population on the earth. This problem of parameter estimation can be solved by one of the below two ways:

1) Point Estimation

2) Interval Estimation

 

 

1) Point Estimation:

    When we aggregate out (summarize) our sample to come up with one number, this number is called point estimation for the entire population.

 

    Example:

       Consider we are given 10 students marks and by looking at these 10 students marks, we need to predict what would be the average marks of all the students of a College.

       [8, 7, 5, 9, 7, 10, 6, 7, 8, 8]

              

       Let us understand and solve this problem:

       

       We are provided with a Sample having Sample size i.e. ‘n’ = 10

       And we need to predict / interpret the average marks of all the students of College i.e. we need to come up with an estimated parameter which is close enough with the actual Population mean (mu)

      

       Let us sum them up and take average:

       8 + 7 + 5 + 9 + 7 + 10 + 6 + 7 + 8 + 8 = 75

       Estimated parameter = 75 / 10 = 7.5

 

       7.5 would be the average marks of all the students of College. It is the point estimate for the population parameter.

 

Advantages of this approach:

      - Easy to calculate

Disadvantages:

     - We are not sure how accurate is this point estimated parameter

 

   Hence, there is a better estimation technique called Interval Estimation which provides an estimation range called as confidence interval with some confidence level.

 

2) Interval Estimation:

    While deriving / summarizing our sample, if we define one estimated range instead of point estimation, then this is considered as an Interval Estimation. 

 

     In the next article we will be discussing about the confidence interval and we will explain both the ways with example:

 

     - Estimating parameter when population standard deviation is given

     - Estimating parameter when population standard deviation is not given