Data, Graphs, and Statistical Measures

Vocabulary flashcards covering key concepts, data types, graphical representations, and statistical measures from Math 251 Unit 1A.

Statistics

The study of data and variation.

Data

Systematically recorded information.

Variation

The concept that data values will be different from subject to subject.

Population

The entire collection of subjects about which information is desired.

Sample

A subset of the population used to gather information.

Observational Unit

Each member of the sample (also referred to as a case, individual, or subject).

Population Parameter

A measure of the population, such as the population mean, represented by the symbol $\mu$.

Sample Statistic

A measure of the sample, such as the sample mean, represented by the symbol $\bar{x}$.

Quantitative Variable

A variable that uses numerical values that are quantities and can be operated upon.

Discrete Variable

A quantitative variable with a countable number of values (e.g., number of people, plants, or cars).

Continuous Variable

A quantitative variable that is measurable (e.g., cost, pulse rate, temperature, weight).

Categorical Variable

A variable that uses labels or groups that are not quantities.

Binary Variable

A categorical variable that has only two labels or categories (e.g., Yes/No).

Non-binary Variable

A categorical variable that can have more than two labels.

Bar Chart

A display used to show counts or percentages for categorical data, characterized by space between bars.

Circle Graph

A display used to show counts or percentages for categorical data, which should be labeled with percentages.

Frequency Table

A display used to organize raw data showing categories, tallies, frequencies, and relative frequencies.

Dot Plot

A visual display best used for small data sets with a small range that shows the distribution of discrete values and gaps in data.

Stem/Leaf Plot

A display best used for small data sets with two digits, where original data values are preserved and it is quick to construct.

Histogram

A display best used for a large range and large data set where the overall distribution shape is clear.

Frequency Histogram

A histogram showing actual counts for each variable value on the vertical axis.

Relative Frequency Histogram

A histogram showing the proportion or percentage for each variable value on the vertical axis.

Skewed Right Distribution

A distribution where most data values are low and a few are high, resulting in a mean greater than the median.

Skewed Left Distribution

A distribution where most data values are high and a few are low, resulting in a mean less than the median.

Symmetric Distribution

A distribution where data values are relatively equal on both sides of the center, resulting in a mean approximately equal to the median.

Bimodal Distribution

A distribution displaying two distinct peaks.

Uniform Distribution

A distribution where all outcomes have a relatively equal probability or frequency.

Mean

The arithmetic average of all data values, represented by $\mu$ for a population and $\bar{x}$ for a sample.

Median

The middle value in a data set, also referred to as the 2nd quartile $Q_2$ or 50th percentile $P_{50}$.

5 Number Summary

The five key numeric summaries of a dataset: Minimum, $Q_1$ (first quartile), Median ($Q_2$), $Q_3$ (third quartile), and Maximum.

Range

A single value measure of spread calculated as $\text{Maximum} - \text{Minimum}$.

IQR (Interquartile Range)

A single value measure of spread calculated as $Q_3 - Q_1$.

Boxplot

A graphical display of data using the 5 number summary; referred to as a modified boxplot when outliers are explicitly displayed.

Outliers

Unusually large or small data values that fall outside calculated lower or upper fences.

Standard Deviation

A measure of the average amount of deviation from the mean among data values (population $\sigma_x$, sample $s_x$).

Variance

The square of the standard deviation ($\sigma^2$ for population, $s^2$ for sample), representing the value before taking the square root.

Resistant Measures

Statistical measures that are not affected by extreme data values.

Non-resistant Measures

Statistical measures that are affected by extreme data values.

Z Score

A standardized score indicating how a single value compares to the whole distribution in terms of position, calculated as $z = \frac{\text{individual value} - \text{mean}}{\text{st. deviation}}$.

Empirical Rule

A rule stating that for symmetric normal models, approximately 68% of data fall within 1 standard deviation of $\mu$, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

Normal Curve

A theoretical, symmetric, mound-shaped distribution model for continuous data where the total area under the curve equals 1.00 or 100%.