If your numbers are every member of the group you care about, choose Population and the variance divides by N. If they are a sample used to estimate a larger group, choose Sample and the variance divides by n − 1 (Bessel's correction), which corrects the tendency of a sample to underestimate spread.
Quartiles use the median-of-halves method taught in most textbooks and used by TI-83/84 calculators: Q1 is the median of the lower half and Q3 the median of the upper half, leaving out the overall median when n is odd. Values more than 1.5 × IQR below Q1 or above Q3 are flagged as outliers and drawn as separate points on the box plot.
The least-squares line ŷ = mx + b is the line that makes the sum of squared vertical distances to the points as small as possible. The correlation coefficient r (from −1 to 1) measures how close the points are to a straight line, and r² is the share of the variation in y explained by x.
For continuous distributions (normal, t, exponential, uniform) probability is the area under the curve, so P(X < a) and P(X ≤ a) are equal. For discrete distributions (binomial, Poisson) probability sits on whole numbers, so < and ≤ give different answers — the bar chart highlights exactly which values are counted.