Numerical characteristics of random variables
The population is all values of a random variable and a sample is a chosen part of it. The mode is the value with the greatest frequency, the median is the middle number of the ordered sample (for an even count, the mean of the two middle ones), and the range is the difference of the largest and smallest values. For X with probabilities p₁, ..., p_k the expected value is E = x₁p₁ + x₂p₂ + ... + x_kp_k. The deviation of a value from the mean X̄ is x − X̄, and the deviations always add up to zero; so we take the mean of their squares, called the variance D: D = ((x₁ − X̄)² + ... + (x_n − X̄)²) : n. The variance has the square of the unit, so the standard deviation σ = √D is used: it has the same unit as X. In a frequency table each square is multiplied by its frequency and the total is divided by the sum of the frequencies.
“Step counts”: 8 students write down how many steps they take over the same distance; the class together computes mode, median, mean, range and variance.