Standard Scores and the Normal Distribution

These flashcards cover vocabulary and concepts related to standard scores and the normal distribution, which are essential for understanding statistics.

Standard Score

A score that has been transformed to provide context for interpretation, often referred to as a z-score.

Z Score

A z score indicates how many standard deviations a score is from the mean; positive z scores are above the mean, while negative z scores are below.

Normal Distribution

A type of distribution that is symmetrical and described by its mean and standard deviation, where most observations cluster around the mean.

Mean

The average of a set of scores, serving as the center point in the normal distribution.

Standard Deviation

A measure of how spread out the scores are in a data set; it quantifies the amount of variation in a set of scores.

Percentile Rank

A score that indicates the relative standing of a score in a frequency distribution compared to others.

Normal Curve Characteristics

Symmetrical in shape, where frequencies decrease as one moves away from the midpoint, which is the mean, median, and mode.

Critical Z Scores

Z scores that mark particular percentiles in a distribution, such as -1.96 and +1.96, corresponding to a 95% confidence interval.

Transformation Formula for Z Score

Z = (X - M) / S, where X is the raw score, M is the mean, and S is the standard deviation.

Transformation Formula for Raw Score

X = (z * S) + M, where z is the z score, S is the standard deviation, and M is the mean.

Area Under Normal Curve

Represents the percentage of observations that fall within a certain range of z scores in a normal distribution.

Empirical Rule

A rule stating that in a normal distribution, approximately 68% of data falls within one standard deviation from the mean, 95% within two, and 99.7% within three.

Bell Curve

A common shape for the normal distribution, illustrating the probability of occurrences of a variable.

Abnormality Cut-off Points

Values beyond which a score is considered significant or abnormal, often set outside of +/- 1.96 in a Z-score context.

Frequency Polygon

A graphical representation of the distribution of scores, creating a shape that typically resembles a bell curve.

Statistical Population Assumption

The assumption that data will follow a normal distribution within the studied population.