Question

Suppose there were 20 quizzes during your statistics course. What would be the advantages and disadvantages of using the trimmed mean to compute your quiz average? (Source our textbook )

Answer 1

We know that,

Using trimmed means confers two advantages:

• trimmed means provide a better estimation of the location of the bulk of the observations than the mean when sampling from asymmetric distributions;
• the standard error of the trimmed mean is less affected by outliers and asymmetry than the mean, so that tests using trimmed means can have more power than tests using the mean.

Disadvantages:-

1. The truncated mean uses more information from the distribution or sample than the median, but unless the underlying distribution is symmetric, the truncated mean of a sample is unlikely to produce an unbiased estimator for either the mean or the median.

2. If we use a trimmed mean in an inferential test (see below), we make inferences about the population trimmed mean, not the population mean.

Thank you.