Question

1) If you computed the 20% Trimmed mean on a data set with 50 values, how many values would you exclude, or throw away in total?

2) Why do people calculate a trimmed mean, anyway?

3) Calculate the Harmonic Mean for the values: 1, 2, 50, 200.

Answer 1

Q1) As we are computing the 20% trimmed mean here, therefore we remove 20/2 = 10% of the observations from both the sides and then compute the mean of the remaining values to get the 20% trimmed mean here. As the total dataset size here is n = 50, the total number of values that would be excluded or thrown away before computing the mean is computed as:
= 0.2*50 = 10

Therefore 10 values would be taken away here before computing the mean to get the required trimmed mean value.

Q2) We calculate the trimmed mean to remove the outlier effect on the mean. Trimmed mean helps in removing the extreme outlier values from both sides of the dataset ( lower and higher values )

Q3) The harmonic mean for the given values here is computed as:

= Reciprocal of the average of the reciprocals means

Therefore 2.6230 is the required harmonic mean here.