sample size, mean, median

[logistic_guy]

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

\(\displaystyle 3.4 \ \ \ 2.5 \ \ \ 4.8 \ \ \ 2.9 \ \ \ 3.6\)
\(\displaystyle 2.8 \ \ \ 3.3 \ \ \ 5.6 \ \ \ 3.7 \ \ \ 2.8\)
\(\displaystyle 4.4 \ \ \ 4.0 \ \ \ 5.2 \ \ \ 3.0 \ \ \ 4.8\)

Assume that the measurements are a simple random sample.

\(\displaystyle \bold{(a)}\) What is the sample size for the above sample?
\(\displaystyle \bold{(b)}\) Calculate the sample mean for these data.
\(\displaystyle \bold{(c)}\) Calculate the sample median.
\(\displaystyle \bold{(d)}\) Plot the data by way of a dot plot.
\(\displaystyle \bold{(e)}\) Compute the \(\displaystyle 20\%\) trimmed mean for the above data set.
\(\displaystyle \bold{(f)}\) Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?

 

[khansaheb]

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

\(\displaystyle 3.4 \ \ \ 2.5 \ \ \ 4.8 \ \ \ 2.9 \ \ \ 3.6\)
\(\displaystyle 2.8 \ \ \ 3.3 \ \ \ 5.6 \ \ \ 3.7 \ \ \ 2.8\)
\(\displaystyle 4.4 \ \ \ 4.0 \ \ \ 5.2 \ \ \ 3.0 \ \ \ 4.8\)

Assume that the measurements are a simple random sample.

\(\displaystyle \bold{(a)}\) What is the sample size for the above sample?
\(\displaystyle \bold{(b)}\) Calculate the sample mean for these data.
\(\displaystyle \bold{(c)}\) Calculate the sample median.
\(\displaystyle \bold{(d)}\) Plot the data by way of a dot plot.
\(\displaystyle \bold{(e)}\) Compute the \(\displaystyle 20\%\) trimmed mean for the above data set.
\(\displaystyle \bold{(f)}\) Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?

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[logistic_guy]

\(\displaystyle \bold{(a)}\) What is the sample size for the above sample?

\(\displaystyle \textcolor{blue}{n = 15}\)

 

[logistic_guy]

\(\displaystyle \bold{(b)}\) Calculate the sample mean for these data.

\(\displaystyle \overline{x} = \frac{3.4 + 2.5 + 4.8 + 2.9 + 3.6 + 2.8 + 3.3 + 5.6 + 3.7 + 2.8 + 4.4 + 4.0 +5.2 + 3.0 + 4.8}{15} = \textcolor{blue}{3.787}\)

 

[logistic_guy]

\(\displaystyle \bold{(c)}\) Calculate the sample median.

\(\displaystyle 2.5, 2.8, 2.8, 2.9, 3.0, 3.3, 3.4,\textcolor{red}{3.6}, 3.7, 4.0, 4.4, 4.8, 4.8, 5.2, 5.6\)

Then,

\(\displaystyle \text{median} = \textcolor{blue}{3.6}\)