Complex sentence: A test statistic is a scalar function of all the observations, such as the average or the correlation coefficient, which summarizes the characteristics of the data by a single number, relevant to a particular inquiry.
Split into simpler sentences: A test statistic is a scalar function of all the observations. This statistic provides a single number, such as the average or the correlation coefficient, that summarizes the characteristics of the data, in a way relevant to a particular inquiry.