General Mathematics 11: Data Types, Levels of Measurement, Central Tendency, and Variability

Vocabulary practice flashcards covering data collection types, Stanley Smith's four levels of measurement, measures of central tendency, and measures of variability from General Mathematics Grade 11 lessons.

Data

Raw facts or information collected for reference or analysis.

Surveys

A source of data gathered by asking people questions to know their opinions or preferences.

Experiments

A source of data collected by performing controlled tests to observe results.

Observations

A source of data obtained by watching and recording behaviors or events as they happen.

Qualitative Data

Categorical, non-numerical data that describes qualities or characteristics.

Quantitative Data

Numerical data that uses numbers and can be measured or counted.

Discrete Data

Quantitative data gathered by counting.

Continuous Data

Quantitative data gathered by measuring.

Measurement (Statistical)

The systematic process of assigning values or labels to data collected according to a defined scale, based on a theory developed in 1946 by Harvard psychologist Stanley Smith.

Nominal Level

The simplest level of qualitative measurement ('existing in name only') used solely for classification or identification purposes, where assigned numbers have no meaningful numerical value.

Ordinal Level

A qualitative level of measurement that indicates the ranks or positions of items using ordinal numbers, without quantifiable differences between the ranks.

Interval Level

An ordered, numerical quantitative level of measurement where distances between values have a clear and constant meaning, but which lacks a true, non-arbitrary zero point.

Ratio Level

The most sophisticated quantitative level of measurement, featuring an inherent order, measurable scales between values, and a true zero point.

Measures of Central Tendency

Statistical tools that describe the center or typical performance of a dataset.

Mean

A measure of central tendency appropriate for interval and ratio data without significant outliers, useful when data are approximately symmetric.

Median

A measure of central tendency representing the center position of ordered data, appropriate for ordinal, interval, and ratio levels and resistant to extreme values.

Mode

A measure of central tendency representing the most frequently occurring value or response in a dataset, applicable to categorical data.

Measures of Variability

Statistical measures that describe how spread out or scattered values in a dataset are from one another or from the center.

Range

A measure of variability calculated as the difference between the highest value and the lowest value in a dataset ($\text{Range} = \text{Highest Value} - \text{Lowest Value}$).

Variance

A measure of variability that measures how far data values are spread from the mean, calculated as the average of the squared deviations from the mean.

Standard Deviation

A measure of variability representing the typical distance of data values from the mean, calculated as the square root of the variance.

Interquartile Range (IQR)

A measure of variability that measures the spread of the middle $50\%$ of data, calculated as the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$) ($\text{IQR} = Q_3 - Q_1$).