What indicates the number of individual scores that can vary without changing the sample mean?

The concept of degrees of freedom is fundamental in statistics, particularly in the context of analyzing samples and the constraints that govern them. When calculating the mean of a sample, the degrees of freedom indicate how many independent values can vary freely before the mean becomes fixed. Specifically, when you have a sample of size n, the degrees of freedom is typically n - 1 in situations like estimating the sample variance.

For example, if you have a set of scores and you know the mean of that set, if you change n - 1 of those scores, the last score will be determined by the requirement to keep the mean constant. This illustrates the core idea: only n - 1 scores can be independently varied without affecting the overall mean.

This concept applies to various statistical analyses, including t-tests and ANOVA, where degrees of freedom play a crucial role in determining the appropriate distribution to use for hypothesis testing. Other options like sample variability, variation potential, and freedom of measurement do not directly address the relationship between individual scores and the sample mean in the established framework of degrees of freedom. Consequently, the correct indication of the number of scores that can vary while keeping the sample mean constant is indeed degrees of freedom.