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 _____.