Introductory Statistics: Standard Deviation, Z-Scores, Histograms, and Box Plots

Vocabulary flashcards reviewing concepts of sample standard deviation, z-score calculations, histograms, class boundaries, and five-number summaries for box plots.

Sample Standard Deviation ($s$)

The square root of the average squared distance a data value is from the mean in a sample, calculated using the formula $s = \sqrt{\frac{\sum (x - \bar{x})^2}{n - 1}}$.

Z-score

A standard measurement describing how many standard deviations a data value lies away from the mean, calculated as $z = \frac{x - \bar{x}}{s}$ for samples or $z = \frac{x - \mu}{\sigma}$ for populations.

Negative Z-score

A z-score with a value less than zero, indicating that the corresponding data value lies below or is smaller than the mean.

Positive Z-score

A z-score with a value greater than zero, indicating that the corresponding data value lies above or is larger than the mean.

Class Boundary

The halfway point between two adjacent classes in a group frequency distribution table, placed along the horizontal axis of a histogram.

Class Width

The number of unique data values that can fit into a single class, found by subtracting consecutive lower class limits or consecutive upper class limits.

Histogram

A visual representation of quantitative data generated from a group frequency distribution table, where touching vertical bars represent frequencies along the vertical axis and class boundaries lie along the horizontal axis.

Box Plot

Also called a box and whisker plot, a graph displaying quantitative data using vertical lines for the five-number summary with a central box and extended whiskers.

Five-Number Summary

A group of five statistical values representing a quantitative dataset, consisting of the minimum data value, first quartile, median, third quartile, and maximum data value.