The chi-square value is obtained in the usual fashion for two-way tables. For each cell, the distance between the observed and expected counts is squared, then divided by the expected value. Finally, these quantities are summed across all cells. For this table, the value is 12.4.

- Degrees of freedom for the frequency table are equal to (rows - 1) * (columns - 1). In this case, that is 1 * 2 = 2.

- The asymptotic significance tells us how often we can expect a chi-square value at least as large as 12.4 in similar repeated samples, if there really is no relationship between the median and group membership. The probability is very low: about two times per thousand.

From this analysis, the manager learns that type of training resulted in different median scores between the groups. Trainees who received the hands-on tutorial have a higher median value than either their counterparts who received standard training or additional technical training.