Variability and z-scores

Calculating z-score

Calculating raw value

What does z-score tell you?

The z-score indicates how many standard deviations a data point is from the mean of the data set. It helps identify the relative position of a value within a distribution.

What us the 68-95-99.7 rule?

The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, approximately 68% of the data points fall within one standard deviation of the mean, about 95% fall within two standard deviations, and roughly 99.7% fall within three standard deviations.

What are the two measures of variability?

Variance and Standard deviation

Equation for variance

(SS / N - 1) — where SS is the sum of squares and N is the number of observations.

Equation for Standard Deviation

(√(SS / N - 1)) — the square root of the variance.

Deviation and squared deviations

the amount that a single raw score deviates from the mean (x - M), then squared to make all values positive (squared deviations)

“SS”

sum of squared deviations