3.B Central Tendency and Variation

Mean, median, and mode all try to answer the same question: what's a typical score here? The mean adds every value and divides by how many there are, so it uses all the information but is sensitive to extreme scores. The median is the middle value once scores are lined up in order, so it only cares about position, not size. The mode is just whichever value shows up most. In a symmetric distribution these three sit close together. As a distribution gets skewed, the mean gets pulled toward the tail (the extreme scores) while the median stays put, so the gap between them grows. That gap is itself a clue about skew.

Variation measures tell you how much the scores disagree with each other. Range is the crudest version: highest score minus lowest. Standard deviation is more useful because it looks at every score's distance from the mean, squares those distances (so negatives don't cancel positives), averages them, and takes a square root to get back to the original units. A small standard deviation means scores cluster tightly around the mean; a large one means they're scattered.

This topic matters because every later unit asks you to interpret data, and the first move is always picking the right summary. A skewed distribution with one wild outlier should be described with the median, not the mean, which is why researchers report both when reaction times, incomes, or reading scores have long tails. Standard deviation then sets up z-scores and the normal curve, where 'typical distance from the mean' becomes the ruler for everything else.