In the mathematical formula for the mean ($M = \frac{\Sigma X}{N}$), what does the symbol $N$ represent?

A psychologist is using the formula $M = \frac{\Sigma X}{N}$ to analyze the results of a memory experiment involving 30 participants. Match each component of the formula to its specific conceptual role in this research context.

Based on the formula $M = \frac{\Sigma X}{N}$, if a researcher realizes they accidentally omitted a score of 0 from their dataset, the sum of scores ($\Sigma X$) will remain the same while the calculated mean ($M$) will decrease because the total number of scores ($N$) has increased.

A psychologist is evaluating whether a data entry error ($X = 100$ instead of $X = 10$) has rendered their sample mean ($M = 50$) misleading. Arrange the steps of this critical evaluation process in the correct logical order based on the components of the formula $M = \frac{\Sigma X}{N}$.

In the mathematical formula for the statistical mean ($M = \frac{\Sigma X}{N}$), the Greek letter sigma ($\Sigma$) represents the summation sign indicating to add all values of the variable $X$.

In psychology research, when a researcher applies the formula for the statistical mean, $M = \frac{\Sigma X}{N}$, what does the mathematical operation of dividing the sum of the scores ($\Sigma X$) by the total number of scores ($N$) conceptually achieve?

A psychologist is analyzing the number of items correctly recalled by a sample of 5 participants in a memory study. The scores are: 12, 18, 10, 14, and 11. Using the statistical mean formula $M = \frac{\Sigma X}{N}$, the mean number of items recalled by this sample is _____.

A cognitive psychology researcher is studying problem-solving speeds and records the completion times (in minutes) for a sample of three participants: 12, 15, and 18. Apply the statistical mean formula $M = \frac{\Sigma X}{N}$ to this dataset by matching each mathematical symbol to its corresponding calculated numerical value.

A psychology researcher is analyzing how an extreme high outlier score distorts a dataset. Based on the components of the statistical mean formula ($M = \frac{\Sigma X}{N}$), arrange the logical cascade of mathematical effects that occur when a single, exceptionally high outlier score is added to a typical distribution.

Two psychology students are determining how to calculate the overall mean reaction time for two combined groups of participants (Group A has 10 participants, Group B has 50 participants). Student 1 argues they should simply add the two group means together and divide by 2. Student 2 argues this is flawed because, according to the formula $M = \frac{\Sigma X}{N}$, they must instead find the grand sum of all individual scores and divide by 60.

Based on your critical evaluation of the statistical mean formula, which student presents the correct methodology and what is the proper mathematical justification?