If the value of \( 5 S \) stays constant, what will happen to the sample variance if the degrees of freedom is increased? (A) no effect (B) increase (C) decrease : (D) none of these Ouestion 6

When the degrees of freedom in a variance calculation increase, it typically means that the sample size is growing. In this situation, since \( 5S \) remains constant, the variability of the data can actually become more stable because averaging over a larger sample tends to reduce the effect of outliers. Therefore, if you increase the degrees of freedom, the sample variance will decrease, as it will reflect a more accurate estimate of the population variance. Additionally, increasing the degrees of freedom gives your estimate of variance more robustness. The more data points you have, the less influenced the variance will be by a few extreme values. This results in a reduced variance estimate, reinforcing the reliability of your data analysis.