Descriptive Statistics - Chapter 3 (VOCABULARY Flashcards)

Vocabulary flashcards covering central tendency, variability, shape, distribution, and basic descriptive statistics concepts from Chapter 3 notes.

Mode

The most frequently occurring value in a data set; may not exist or may be bimodal or multimodal; applicable to all levels of data.

Median

The middle value in an ordered data set; for an even number of observations, the average of the two middle terms; not affected by extreme values.

Mean (Arithmetic Mean)

The average of a group of numbers; includes all data in the set; a common measure of central tendency.

Population Mean (μ)

The average of a population; a parameter that describes the entire group.

Sample Mean (x̄)

The average of a sample; a statistic used to estimate the population mean.

Percentile

A value below which a certain percentage of data fall; e.g., the nth percentile has at least n% of data at or below it.

Pth Percentile Calculation

To find the Pth percentile: order data, locate the percentile position (i = p/100 * N), and average the surrounding values if needed (or round up when the position is not whole).

Quartiles

Five-number summary that divides data into four parts; Q1 (25th percentile), Q2 (median), Q3 (75th percentile); Q2 equals the median.

First Quartile (Q1)

The 25th percentile of the data.

Second Quartile (Q2) / Median

The 50th percentile; the middle value of the ordered data.

Third Quartile (Q3)

The 75th percentile of the data.

Interquartile Range (IQR)

The spread of the middle 50% of the data; IQR = Q3 − Q1.

Range

The difference between the largest and smallest values in a data set; easy to compute but affected by outliers.

Variance (Population)

The average of the squared deviations from the population mean; measured in squared units.

Variance (Sample)

An unbiased estimator of the population variance, computed with denominator n−1.

Standard Deviation (Population)

The square root of the population variance; measures spread in the same units as the data.

Standard Deviation (Sample)

The square root of the sample variance; used to estimate population variability.

Mean Absolute Deviation (MAD)

The average distance between each data value and the mean; a measure of spread using absolute deviations.

Empirical Rule (68-95-99.7)

For normally distributed data: about 68% within 1 SD, 95% within 2 SD, and 99.7% within 3 SD of the mean.

Chebyshev’s Theorem

For any distribution, at least (1 − 1/k^2) of data lie within k standard deviations of the mean (k>1).

Skewness

A measure of asymmetry in a distribution; skewness can be left (negative) or right (positive).

Kurtosis

A measure of the peakedness or flatness of a distribution.

Box-and-Whisker Plot

A graphical representation of a distribution using the min, Q1, median, Q3, and max; includes whiskers and outlier detection via fences.

Five-Number Summary

The minimum, Q1, median, Q3, and maximum used to construct a box plot.

Outlier

A value that falls outside the inner fences of a box plot; can be mild (within outer fences) or extreme (beyond outer fences).

Inner Fences

Boundaries at Q1 − 1.5·IQR and Q3 + 1.5·IQR used to identify mild outliers.

Outer Fences

Boundaries at Q1 − 3·IQR and Q3 + 3·IQR used to identify extreme outliers.

Hinges

The endpoints of the box in a box plot, corresponding to Q1 and Q3.

Z-Score

The number of standard deviations a value is from the mean; z = (x − μ)/σ for a population, or (x − x̄)/s for a sample.

Coefficient of Variation (CV)

The ratio of the standard deviation to the mean, expressed as a percentage; used to compare variability across datasets with different scales.

Symmetry of Mean, Median, and Mode

In a symmetric distribution, mean = median = mode; skewness affects their ordering (negative or positive skew).

Normal Distribution

Bell-shaped, symmetric distribution where empirical rules and standard deviation-based inferences apply.

Box Plot Utility in Shape Assessment

Box plots help assess skewness and identify outliers by examining the median position and whisker lengths.