Answer:
> x<-c(67, 68, 64, 61, 65, 64, 70, 67, 62, 63, 61, 64, 75, 67, 60, 59, 64, 68, 65, 71)
> length(x)
[1] 20
> mean(x, trim = 0.2)
[1] 65
Step-by-step explanation:
For this case we have the following dataset:
67 68 64 61 65 64 70 67 62 63 61 64 75 67 60 59 64 68 65 71
We can calculate the trimmed mean by hand or using R. For the first case we need to order the data on increasing way like this:
59 60 61 61 62 63 64 64 64 64 65 65 67 67 67 68 68 70 71 75
Now since we need the 20% trimmed mean we need to remove 10% of the data for the upper and the lower tail. Since we have 20 data values 20*0.1=2 observations are required to remove for each tail so our new dataset would be:
61 61 62 63 64 64 64 64 65 65 67 67 67 68 68 70
And we can calculate the trimmed mean using the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{16} =65[/tex]
And if we use R we can use the following code:
> x<-c(67, 68, 64, 61, 65, 64, 70, 67, 62, 63, 61, 64, 75, 67, 60, 59, 64, 68, 65, 71)
> length(x)
[1] 20
> mean(x, trim = 0.2)
[1] 65
And as we can see both results are the same.
