Problem 1.1| Introduction to Statistics and Data Analysis| Probability & Statistics for Engineers & Scientists 8th Ed| Walpole, Myers, Myers, Ye

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

3.4

2.5

4.8

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 of 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

The sample size is 15.

Part b

\overline{x}=\frac{1}{15}\left(3.4+2.5+4.8+2.9+3.6+2.8+3.3+5.6+3.7+2.8+4.4+4.0+5.2+3.0+4.8\right)

\overline{x}=3.787

Part c

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

Part d

A dotplot is shown below

Dotplot 1.1d

Part e

After trimming total 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

\overline{x}=\frac{1}{9}\left(2.9+3.0+3.3+3.4+3.6+3.7+4.0+4.4+4.8\right)

\overline{x}=3.678

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