Which type of graph is most effective for smaller data sets of ungrouped quantitative data?

The choice of a dot plot as the most effective graph for smaller data sets of ungrouped quantitative data is particularly well-founded because it allows for precise visualization of individual data points. In a dot plot, each observation is represented by a dot along a number line, making it easy to see the distribution and frequency of specific values without any loss of detail.

For smaller data sets, where the number of data points is limited, a dot plot effectively communicates the shape and spread of the data. It demonstrates how frequently each value occurs, making it possible to quickly identify trends, clusters, and outliers. This clarity can be particularly valuable when analyzing detailed data points or comparing values.

Additionally, dot plots maintain the exact value of each observation, which is crucial when dealing with smaller datasets. Other types of graphs, like bar charts and pie charts, aggregate or group data, which can obscure individual data points and their specific values. Thus, while those types of graphs can be more effective for larger or categorical data sets, they are not as suitable for ungrouped quantitative data that comprises fewer observations.