A z-score, also known as a standard score, indicates how many standard deviations a data point is from the mean of a dataset. Calculating this value using a TI-84 graphing calculator involves inputting data and utilizing the calculator’s statistical functions. For instance, if one seeks to determine how a student’s test score compares to the class average, a z-score can quantify the student’s performance relative to the distribution of scores.
Calculating and understanding standard scores offers significant benefits in statistical analysis. It allows for standardization and comparison of data from different distributions. Historically, this calculation facilitated quality control in manufacturing and continues to be crucial for hypothesis testing and interpreting results in fields such as psychology, economics, and engineering. A z-score enables the determination of the probability of a certain value occurring within a normal distribution, providing valuable insights for decision-making.