Chapter 2: Summarizing Data

Flashcards covering vocabulary and key concepts for summarizing numerical and categorical data from Chapter 2.

Dot plot

A graph that shows a dot for each observation, placed just above the value on the number line for that observation.

Skewed right

A distribution shape characterized by a few unusually large measurements.

Skewed left

A distribution shape characterized by a few unusually small measurements.

Bimodal

A distribution shape that has two local peaks.

Outliers

Strange or unusual measurements that stand out in the data set.

Histogram

A graphical display similar to a dot plot where values are put into bins and bars are drawn with heights equal to their frequency or relative frequency.

Left inclusion

The method of constructing histogram intervals that includes the left endpoint but not the right in the tally.

Parameter

A numerical descriptive measure calculated for a population.

Statistic

A numerical descriptive measure calculated for a sample.

Arithmetic Mean

The sum of the measurements divided by the total number of measurements, represented by the formula $\bar{x} = \frac{\sum x_i}{n}$.

Population Mean (mu)

The mean of an entire enumerated population, denoted by the Greek letter $\mu$.

Median

The middle measurement when measurements are ranked from smallest to largest; its position is located at $.5(n + 1)$.

Mode

The measurement which occurs most frequently in a data set.

Range

The difference between the largest and smallest measurements in a set, denoted as $R$.

Variance

A measure of variability that uses all measurements to calculate the average deviation about their mean.

Sample Variance

The sum of squared deviations of measurements about their mean divided by $(n - 1)$, denoted as $s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}$.

Standard Deviation

The positive square root of the variance, used to return the variability measure to the original units of measure.

Percentiles

Values of the variable that divide a set of ranked data into $100$ subsets containing an equal number of data.

First Quartile (Q1)

The $25^{th}$ percentile: the value of $x$ which is larger than $25\%$ and less than $75\%$ of the ordered measurements.

Third Quartile (Q3)

The $75^{th}$ percentile: the value of $x$ which is larger than $75\%$ and less than $25\%$ of the ordered measurements.

Interquartile Range (IQR)

The range of the middle $50\%$ of the measurements, calculated as $IQR = Q3 - Q1$.

Robust Statistics

Numerical measures such as the median and IQR that are little affected by extreme observations.

Five-Number Summary

A data summary consisting of the Minimum, $Q1$, Median, $Q3$, and Maximum.

Box Plot

A graph involving a box from $Q1$ to $Q3$ and whiskers used to describe the distribution shape and detect outliers.

Lower fence

A boundary used to identify outliers, calculated as $Q1 - 1.5 \times IQR$.

Upper fence

A boundary used to identify outliers, calculated as $Q3 + 1.5 \times IQR$.

Log transformation

A common data transformation used to reduce skew, assist in modeling, or straighten nonlinear relationships.

Summary Table

A basic table that summarizes a categorical variable by showing the frequency or count of each category.

Bar Plot

A common way to display a single categorical variable where bars represent frequencies or proportions.

Pie Chart

A circle divided into sectors where the area of each sector is proportional to the frequency of the category.

Contingency Table

A table that summarizes data for two categorical variables simultaneously.

Stacked Bar Plot

A visualization that takes a one-variable bar plot and breaks up the bars to show a second categorical variable.

Side-by-side Bar Plot

A visualization that takes a one-variable bar plot and splits each bar into two side-by-side bars for a second variable.

Mosaic Plot

A graphical display used for one or two categorical variables where the area of rectangles represents the proportion of observations.

Side-by-side Box Plots

Standard tools used to visualize and compare numerical data broken down into categories.

Hollow Histograms

Histograms that allow for the visualization of two distributions layered on top of each other.