Question

Data Set A:

1.32, 1.01, 0, 2.21, 1.69, 1.73, 2.01, 0, 0.73, 0.91, 0, 3.03, 2.22, 1.23, 3.71, 0, 0.45, 2.18, 3.12, 1.91

Data Set B:

0, 0.63, 2.11, 1.37, 0, 1.11, 2.93, 0, 3.11, 2.61, 0, 0.38, 0.98, 1.55, 1.83, 0, 3.46, 2.31, 0, 1.49

- Comment on the Robust(trimming) estimates of central tendency differences.

Answer 1

Two Data sets are given

Sorted Data set A is given as

Remove the first 4 smallest and 4 largest value for finding the 20% trimmed mean which means

(0.2*20=4 observations remove)

20% Trimmed mean will be of only 12 observations

Trimmed mean =(0.45+0.73+......+3.12+3.71)/12 is given as 17.38

Data set A
0
0
0
0
0.45
0.73
0.91
1.01
1.23
1.32
1.69
1.73
1.91
2.01
2.18
2.21
2.22
3.03
3.12
3.71

Similarly 20% trimmed mean for sorted data set B will be

20% Trimmed mean will be 13.76 after removing the first four and last four observations which is also highlighted

Data set B
0
0
0
0
0
0
0.38
0.63
0.98
1.11
1.37
1.49
1.55
1.83
2.11
2.31
2.61
2.93
3.11
3.46

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.