the numerical average. Obtained by summing all of the measurements in the distribution and dividing by the number of measurements in the distribution
Population Mean µ
Sample Mean M
a quantity computed from the scores in a population.
a quantity computed from the scores in a sample.
a quantity which when all possible random samples of the same size are collected from a population and a mean is computed from each of the samples, then the mean of means equals the population parameter being estimated.
the 50th percentile, the score value that has below it half of the measurements in the distribution and half the measurements above it.
the score value (or class interval) with the greatest frequency.
the extent to which the measurements in a distribution differ from one another.
the largest score minus the smallest score.
the average of the squared deviations of each score from the population mean (µ). The symbol for the population variance is the Greek lowercase letter sigma to the power of two,σ².
Sum of Squares (SS)
the sum of the squared deviations of each score.
SS Sum of Squares
Σ(X-μ)² or ΣX² - ((ΣX)²)/N
σ² Population Variance
(∑(X- μ)²)/N or (∑X²-Nµ²)/N
the sum of squared deviations of each score from M divided by n – 1. The symbol of the sample variance is s².
s² Sample Variance
SS/(n-1) or (∑X²-nM²)/(n-1)
Standard Score (z score)
a score that has been standardized by subtracting µ and dividing the difference by σ. This score indicates the number of standard deviations the observation is above or below the mean of the distribution.
z score formula
Raw Score from a zscore formula
A unimodal and symmetrical distribution with both tails extending to infinity.