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The stem-and-leaf display is a graphical method that organizes data to help us quickly interpret its shape and distribution. It's like an expanded histogram, but instead of bars, it uses numbers to summarize data. Each data point is broken down into a "stem" and a "leaf." The stem reflects the higher digit, while the leaf shows the lower digit.

For example, if a population growth rate is 23%, the '2' represents the stem, and the '3' represents the leaf. When you place numbers like this for all data points, you end up with a display where the stems appear as rows and the leaves as the data extending from these rows.

Stem-and-leaf displays are powerful because they retain the original data, which traditional histograms don't. It helps identify patterns, like where most data points fall and whether there are gaps or clusters. In the context of the exercise, a stem-and-leaf display assists in visualizing the distribution of population growth rates for all U.S. states, offering a clear view of how growth rates differ across states.

Population growth refers to the change in the number of people living in a particular region over time. It is often expressed as a percentage change and is a key indicator of how a region evolves demographically. Various factors influence population growth, such as birth rates, death rates, immigration, and emigration.

In analyzing population growth for the U.S. states between 2010 and 2015, you are essentially examining how many more (or fewer) people live in these states within that timeframe. Understanding this change can illuminate broader economic, social, and environmental trends.

By categorizing the states into Eastern and Western regions, we can discern whether specific areas of the country are growing at different rates. This data can serve public policy makers, businesses, and social services, allowing them to plan accordingly.

In any data set, outliers are data points that stand out from the rest. These are usually much higher or lower than the other data points and have the potential to skew the analysis if not properly addressed.

Identifying outliers is essential because they can represent significant anomalies, or errors in data collection. In a stem-and-leaf display, outliers might appear as leaves that are not near any others, which makes them easy to spot.

Connecting to the population growth example, if a state has an extraordinarily high or low growth rate compared to the rest, this would be considered an outlier. Detecting such outliers is crucial since they might indicate unique economic conditions, policy differences, or data collection errors. Therefore, while analyzing the growth rates, recognizing and interpreting these outliers can provide deeper insights into state-by-state growth dynamics.