Final answer:
The value of r in a data set must be compared to critical values from a table to determine its significance, but without the complete question or context, it is impossible to provide the correct value of r among the provided options.
Step-by-step explanation:
To determine the value of r for a given data set rounded to three decimal places, one typically looks at the provided data or the result of a statistical calculation. In our case, examples are given with different r values and contexts of significance based on critical values from a table. However, the question seems incomplete as it does not provide a specific data set or context from which to derive the value of r.
Nonetheless, based on the examples given, we can infer the process. To assess the significance of r, one compares the computed r to critical values for a given degrees of freedom (df), which is often denoted as n - 2 where n is the sample size. If r is greater than the positive critical value or less than the negative critical value, it is deemed significant. For example, if you computed r = -0.624 with 14 data points, you would have df = 12. If the critical values at df = 12 are ±0.532, and since -0.624 < -0.532, the r is significant.
Without a complete question or more context, we cannot confidently determine which of the provided options (-.618, .877, -.877, .618) is the correct value of r for the data set in the initial question.