Question

Reference: Exercise 1.1 

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint. 

3.4 2.54.8 2.9 3.6 

2.8 3.3 5.6 3.7 2.8 

4.4 4.0 5.2 3.0 4.8 

Assume that the measurements are a simple random sample. 

(a) What is the sample size for the above sample? 

(b) Calculate the sample mean for these data. 

(c) Calculate the sample median 

(d) Plot the data by way of a dot plot. 

(e) Compute the 20% trimmed mean for the above data set. 

(f) Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?

Answer 1

Solution:

a) What is the sample size for the above sample?

Answer: The sample size is 15 because there are 15 observations given.

b) Calculate the sample mean for these data.

Answer: The sample mean is given below:

c) Calculate the sample median.

Answer: To find the sample median, we need to sort the data in ascending order as:

Now the median is calculated as:

(d) Plot the data by way of a dot plot.

Answer: The dot plot is given below:  

(e) Compute the 20% trimmed mean for the above data set.

Answer: We first need to trim the top and bottom 20% of the given data. That leaves us with the middle 9 values:

Therefore, the 20% trimmed mean is:

(f) Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?

Answer: Since the sample mean is 3.7867 and trimmed mean is 3.6778, so these are approximately same.