Final answer:
The correlation coefficient, represented as r, is the measure of the strength and direction of a linear relationship between two variables and cannot be determined solely by mean and standard deviation. The coefficient of determination, r², indicates the explained variability. Statistical tools are required to calculate r from raw data.
Step-by-step explanation:
To determine the correlation coefficient when given the mean and standard deviation of a dataset, it is important to understand that neither the mean nor the standard deviation can be used to directly compute this statistic. Therefore, the correct answer to the question is c) Correlation coefficient cannot be determined from mean and standard deviation. The correlation coefficient, often represented as r, is a measure of the strength and direction of a linear relationship between two variables. This statistic ranges from -1 to +1, where +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.
r can be calculated using a variety of statistical tools, including computer spreadsheets, statistical software, and advanced calculators like the TI-83, TI-83+, or TI-84+. These tools use the raw data points from both variables to compute the correlation coefficient. Furthermore, the square of this coefficient, r², known as the coefficient of determination, can be used to understand the proportion of variability in one variable that is explained by the variability in another when using a linear regression. To illustrate, if a sample dataset of students' scores on two different exams shows a correlation coefficient of r = .6631, the r² value would be .4397, or approximately 44% when expressed as a percentage. This means that approximately 44 percent of the variation in one exam score can be explained by the variation in the other score using the linear regression model. Remember, the calculation of the correlation coefficient requires the actual data points and cannot be done with only the mean and standard deviation of the datasets. For any calculations or interpretations, data integrity and sample size are vital factors that complement the correlation coefficient for reliability.