Delay from Group Delay plot type

The plot type Group Delay displays the delay in milliseconds as a function of frequency. In case of a simple impulse response, such as for a sound card, plotting the group delay will give the initial time delay with accuracy better than 1 sample as shown below. The delay can be found by reading the value at the vertical axis at e.g. 1000 Hz. (In the plot below the group delay is smoothed in 1/6 octaves.)But for more complicated impulse responses, the curves are more complicated. Shown below is the result from the measurements used as examples in the sections above. We see that the delay changes somewhat as function of frequency.