After the generation of multimedia data turned digital, an explosion of interest in their data storage, retrieval, and processing has drastically increased. This includes videos, images, and audios, where we now have higher expectations in exploiting these data at hands. Typical manipulations are in some forms of video/image/audio processing, including automatic speech recognition, which require fairly large amount of storage and are computationally intensive. In our recent work, we have demonstrated the utility of time series representation in the task of clustering multimedia data using k-medoids method, which allows considerable amount of reduction in computational effort and storage space. However, kmeans is a much more generic clustering method when Euclidean distance is used. In this work, we will demonstrate that unfortunately, k-means clustering will sometimes fail to give correct results, an unaware fact that may be overlooked by many researchers. This is especially the case when Dynamic Time Warping (DTW) is used as the distance measure in averaging the shape of time series. We also will demonstrate that the current averaging algorithm may not produce the real average of the time series, thus generates incorrect k-means clustering results, and then show potential causes why DTW averaging methods may not achieve meaningful clustering results. Lastly, we conclude with a suggestion of a method to potentially find the shape-based time series average that satisfies the required properties.