Descriptive Statistics: Central Tendency, Variability, and Parameters

Comprehensive vocabulary flashcards reviewing central tendency, variability, skewness, kurtosis, sample statistics, and population parameter estimation.

Scale Variable

A variable containing true numeric measurements that typically has a wider range of values, used as the primary Dependent Variable (DV) in statistical tests.

Descriptive Statistics

Statistical procedures that use a small set of numbers (statistics) to summarize the values collected in a sample.

Inferential Statistics

The process of estimating population parameters based on calculated sample statistics.

Central Tendency

Statistical measures that summarize the values of data points to identify a single representative score for an entire data set.

Mean ($M$)

The arithmetic average of a data set, calculated by summing all data values ($\sum X$) and dividing by the sample size ($N$): $M = \frac{\sum X}{N}$.

Median

The midpoint of a data range, identified by arranging values from smallest to largest and selecting the middle value (or the average of the two middle values).

Mode

The data value that occurs with the highest frequency in a data set.

Skewed Distribution

A distribution characterized by one particularly long tail that pulls the mean toward it, making the median a more representative measure of central tendency than the mean.

Left-Skewed (Negative Skewness)

A distribution in which the long tail extends to the left, causing the mean to be pulled below the median and mode.

Right-Skewed (Positive Skewness)

A distribution in which the long tail extends to the right, causing the mean to be pulled above the median and mode.

Variability

A measure of the spread or dispersion of data points, indicating how far apart scores are from one another and from the center.

Range

A single-number measure of variability calculated by subtracting the lowest value from the highest value in a data set.

Sample Variance ($SD^2$)

A measure of the total amount of squared distances between data points and the sample mean, calculated as $SD^2 = \frac{\sum (X - M)^2}{N}$.

Sample Standard Deviation ($SD$)

A measure of the average distance between an individual score and the sample mean, calculated as $SD = \sqrt{\frac{\sum (X - M)^2}{N}}$.

Kurtosis

A characteristic of data variability that describes how data points distribute toward the center, ranging from a tall, sharp peak with tails to a flat, uniform distribution.

Statistic

A numerical calculation performed on collected sample data to describe sample characteristics and estimate population parameters.

Parameter

A numerical characteristic describing an entire population, which is rarely possible to calculate directly.

Population Parameters Symbols ($\mu$, $\sigma$, $\sigma^2$)

Greek notation representing the true population mean ($\mu$), population standard deviation ($\sigma$), and population variance ($\sigma^2$).

$N - 1$ Adjustment

The mathematical adjustment used in the denominator of variance and standard deviation formulas when estimating population variability from a sample, compensating for the sample's narrower spread.

Estimated Population Variance ($s^2$)

An estimate of the population variance calculated from sample data using $s^2 = \frac{\sum (X - M)^2}{N - 1}$.

Estimated Population Standard Deviation ($s$)

An estimate of the population standard deviation calculated from sample data using $s = \sqrt{\frac{\sum (X - M)^2}{N - 1}}$.