Displaying & Describing Data Part II

Vocabulary flashcards covering measures of location, central tendency, dispersion, variance, standard deviation, and reading distribution plots.

Adolphe Quetelet

Nineteenth-century scholar quoted regarding statistics: "The determination of the average man is not merely a matter of speculative curiosity; it may be of the most important service to the science of man and the social system."

Measures of Location

Statistical values that summarize a data set into a single value at the aggregate level to describe the location of the data.

Measures of Central Tendency

Measures of location that describe the "typical" or "central" value of a data set.

Mean

The sum of all values observed on a variable divided by the total number of values observed on that variable ($\bar{X}$ for sample mean, $\text{μ}$ for population mean); it is influenced by outliers and susceptible to mathematical manipulation.

Dichotomous Variable Mean Formula

The mean calculation for dichotomous variables expressed as $\bar{X} = \frac{N_1}{N} = p_x(1)$, where $p = \text{proportion}$.

Median

The "middle point" or $50\text{th}$ percentile of a data set; it is not influenced by outliers and is not as easily manipulated mathematically as the mean.

Median Location Formula

The formula used to locate the position of the median in an ordered dataset: $\text{Median location} = \frac{N + 1}{2}$.

Mode

The most frequently occurring value on a variable; it is not influenced by outliers and provides no information about other scores except that they occur less frequently.

Unimodal

A dataset or distribution possessing $1$ most frequently occurring value.

Bimodal

A dataset or distribution possessing $2$ most frequently occurring values.

Trimodal

A dataset or distribution possessing $3$ most frequently occurring values.

Multimodal

A dataset or distribution possessing $3$ or more most frequently occurring values.

Measures of Dispersion

Statistics that describe the spread of the data or the amount of variability present in the data.

Range

A measure of dispersion calculated as the difference between the maximum observed value and the minimum observed value: $\text{Range} = X_{\text{max}} - X_{\text{min}}$.

Interquartile Range

A measure of dispersion calculated as the difference between the $75\text{th}$ percentile and the $25\text{th}$ percentile: \text{Interquartile Range} = X_{75\text{th}\text{%}} - X_{25\text{th}\text{%}}.

Deviation Score

The difference between an individual score $X_i$ and the sample mean $\bar{X}$, expressed mathematically as $X_i - \bar{X}$.

Sum of Deviations

The sum of all individual deviation scores from the mean in a distribution, expressed as \text{∑}(X_i - \bar{X}), which always equals $0$.

Average Absolute Deviation

A measure of dispersion calculated as \frac{\text{∑}|(X_i - \bar{X})|}{N}, where the numerator is the sum of absolute deviations from the mean.

Variance (Average Squared Deviation)

A measure of dispersion calculated as s^2 = \frac{\text{∑}(X_i - \bar{X})^2}{N} = \frac{\text{∑}X_i^2 - \frac{(\text{∑}X_i)^2}{N}}{N}, representing average squared deviation from the mean.

Standard Deviation

A measure of dispersion defined as the square root of variance ($s = \text{√}{s^2}$ for sample standard deviation, $\text{σ}$ for population standard deviation).

General-Type Proposition

A proposition asserting something presumably true of each and every member of a designable class (Bakan, 1967).

Aggregate-Type Proposition

A proposition asserting something presumably true of the class considered as an aggregate (Bakan, 1967).

Box and Whisker Plot Skew Determination

To determine skew from a box plot, evaluate two questions: (1) Are there any outliers? (2) Which half of the box is wider?