First order the data sets for both trained and untrained employees.

Trained: \(118, 120, 121, 125, 126, 127, 128, 129, 130, 130, 131, 132, 134, 135, 137\).

Untrained: \(126, 134, 135, 139, 140, 142, 142, 144, 145, 145, 148, 149, 152, 153, 156\).

There are \(\text{15}\) values in each data set.

Using the percentile formula with \(n = 15\), we can find the rank of the \(25^{\text{th}}\), \(50^{\text{th}}\) and \(75^{\text{th}}\) percentiles:

\begin{align*}
{r}_{25} & = \frac{25}{100}\left(15 - 1\right) + 1 \\
& = \text{4,5} \\
{r}_{50} & = \frac{50}{100}\left(15 - 1\right) + 1 \\
& = \text{8} \\
{r}_{75} & = \frac{75}{100}\left(15 - 1\right) + 1 \\
& = \text{11,5}
\end{align*}

For the \(25^{\text{th}}\) percentile the rank is \(\text{4,5}\), which is between the fourth and fifth values. For the \(50^{\text{th}}\) percentile (the median) the rank is \(\text{8}\). Therefore the median lies at the eighth value. For the \(75^{\text{th}}\) percentile the rank is \(\text{11,5}\), meaning between the eleventh and \(12^{\text{th}}\) values.

For the trained employees we get:

\(25^{\text{th}}\) percentile: \(\text{125,5}\); median: 129; \(75^{\text{th}}\) percentile: \(\text{131,5}\).

For the untrained employees we get:

\(25^{\text{th}}\) percentile: \(\text{139,5}\); median: 144; \(75^{\text{th}}\) percentile: \(\text{148,5}\).