Statistics • Continuous Random Variables and the Normal Distribution
Bars show the relative frequency density (relative frequency divided by class width). The smooth line is a continuous curve approximation. The shaded region is the probability for your interval.
It computes the probability that a continuous random variable falls between a and b using grouped class-interval data. The probability is treated as area under a curve over the interval.
Provide three columns: lower bound, upper bound, and either frequency (f) or relative frequency (r). Intervals can also be written as text such as "60 to less than 61" as long as two numbers can be extracted.
For unequal class widths, a histogram should use density so that total area equals 1. Density for a class is computed as r_i / w_i, where r_i is the class relative frequency and w_i is its width.
No, for continuous variables the probability at a single point is 0, so including or excluding endpoints does not change the interval probability. That is why P(a <= X <= b) equals P(a < X < b).
Frequencies are counts per class, while relative frequencies are proportions that sum to 1 across all classes. The calculator can work with either, but you must select the correct value type so the probabilities are scaled properly.