Question

The data below consists of the heights (in inches) of 20 randomly selected women. Find the 20% trimmed mean of the data set. Round to two decimal places. (Do not use Excel. Use R.)

Answer 1

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:

$\bar X = \frac{\sum_{i=1}^n X_i}{16} =65$

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.