Measures of Central Tendency and Dispersion

Flashcards based on key concepts from the lecture notes about measures of central tendency, dispersion, and data analysis.

Mean

The arithmetic average of a set of values, calculated by summing the values and dividing by the number of values.

Median

The middle value of a data set when arranged in ascending order; it divides the data into two equal parts.

Mode

The value that appears most frequently in a data set; a data set may have no mode, one mode, or more than one mode.

Outliers

Unusual data values that differ significantly from other observations in a data set.

Quartiles

Values that divide a data set into four equal parts, with Q1, Q2 (median), and Q3 representing the 25th, 50th, and 75th percentiles, respectively.

Interquartile Range (IQR)

The difference between the third quartile (Q3) and first quartile (Q1), representing the range of the middle 50% of the data.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values.

Population Mean (μ)

The mean of all observations in a population.

Sample Mean (x̄)

The mean calculated from a sample of the population.

Resistant Statistic

A statistical measure that is not significantly affected by extreme values in a data set.

Chebyshev’s Inequality

A theorem stating that for any data set, no more than 1/k² of observations can be more than k standard deviations away from the mean.

Empirical Rule

A statistical rule stating that for a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3.

Z-score

A statistical measurement that describes a value’s relationship to the mean of a group of values, expressed in terms of standard deviations.

Five-Number Summary

A descriptive statistic that provides information about a data set, consisting of the minimum, Q1, median (Q2), Q3, and maximum.

Boxplot

A graphical representation of the five-number summary of a data set, showing its median, quartiles, and potential outliers.