Introduction to Statistics and Data Analysis | Probability & Statistics for Engineers & Scientists | Walpole | Problem 1.1

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

3.42.54.82.93.6
2.83.35.63.72.8
4.44.05.23.04.8

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 this 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.

Solution:

Part a

By direct counting, there are 15 samples. 

Part b

The sample mean, \displaystyle \bar{x}  is calculated as follows:

\displaystyle \bar{x}=\frac{3.4+2.5+4.8+...+4.8}{15}=3.787

Part c

Sample median is the 8th value, after the data is sorted from smallest to largest. The sample median is 3.6.

Part d

A dot plot is shown below

1

Part e

After trimming a total of 40% of the data (20% highest and 20% lowest), the data becomes: 2.9, 3.0, 3.3, 3.4, 3.6, 3.7, 4.0, 4.4, 4.8.

So. the trimmed mean is

\displaystyle \bar{x}_{tr20}=\frac{2.9+3.0+...+4.8}{9}=3.678