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Fur Seals on St. Paul Island. Every year, hundreds of thousands of northern fur seals return to their haul-outs in the Pribilof Islands in Alaska to breed, give birth, and teach their pups to swim, hunt, and survive in the Bering Sea. U.S. commercial fur sealing operations continued on St. Paul until 1984 , but despite a reduction in harvest, the population of fur seals has continued to decline. Possible reasons include climate shifts in the North Pacific, changes in the availability of prey, and new or increased interaction with commercial fisheries that increase mortality. Here are data on the estimated number of fur seal pups born on St. Paul Island (in thousands) from 1979 to 2018 , where a dash indicates a year in which no data were collected:28 II FURSEALS Make a stemplot to display the distribution of pups born per yean. Describe th shape, center, and variability of the distribution. Are there any outliers?

Step by step solution

01

Organize the Data

First, arrange the provided data in increasing order for clarity. Exclude any years where data is missing. This ordered data will be used to construct the stemplot.

02

Create the Stemplot

Use the tens digit of each data point as the stem and the ones digit as the leaf. List stems vertically, then plot leaves horizontally. This graphical representation will display the spread of the data.

03

Describe the Shape of the Distribution

Evaluate the stemplot to determine the overall shape of the distribution. Check for patterns, such as symmetry or skewness, to describe whether the data is skewed to the left, right, or is roughly symmetric.

04

Identify the Center of the Distribution

Find the median of the data set from the stemplot to describe the center. The median is the middle value when data is ordered, which indicates the typical number of pups born per year.

05

Assess Variability

Determine the range, which is the difference between the maximum and minimum values in the data. Additionally, observe the spread of leaves. Large spread indicates high variability, while closely packed leaves indicate low variability.

06

Identify Possible Outliers

Examine the leaves to identify any values that are significantly distant from others. These may indicate outliers, which are unusual values far removed from the rest of the data.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Data Organization

Organizing data is the first step in many statistical analyses, especially when creating visual representations like stemplots. When you have raw data, such as the number of fur seal pups born each year, it's essential to arrange this information in an ordered sequence. This typically means sorting the data from the smallest to the largest values. By doing so, you make it easier to spot trends and patterns, as well as prepare the data for further analysis and graphical displays.

To organize data effectively:

• List all numerical data in ascending order.
• Exclude any partial or incomplete data points, such as years with missing information.

This ordered dataset provides the foundation for creating a stemplot, allowing you to visualize data clearly and concisely.

Distribution Shape

The shape of a data distribution is crucial for understanding its characteristics. The stemplot is a tool that helps represent this shape visually, showing how data points are dispersed over different value ranges. By examining the stemplot, one can identify patterns such as symmetry, skewness, and modality.

Consider these shapes:

• **Symmetric Distribution:** Reflects a balanced spread on both sides of a central value.
• **Skewed Right:** More data points fall on the left side, with a tail extending to the right.
• **Skewed Left:** More points are on the right, and the tail extends to the left.

A clear understanding of the distribution shape aids in predicting the behavior of data, its variability, and whether it contains outliers.

Median

The median is the center of a dataset and represents the middle value when numbers are arranged in ascending order. It provides insight into what a typical data point looks like, especially when compared to the mean or average, which can be skewed by outliers.

To find the median:

• Order the dataset from lowest to highest.
• If the number of data points is odd, the median is the middle number.
• If even, it is the average of the two middle numbers.

This measure is particularly useful for understanding the distribution's center in the presence of skewed data.

Variability

Variability measures how spread out data points are in a dataset. In a stemplot, variability is seen through the range and dispersion of leaves along the stems. A dataset with high variability will have leaves that spread widely from the central values, while low variability means leaves are clustered closely.

Key points to assess variability include:

• **Range:** Difference between the highest and lowest data values.
• **Spread of Leaves:** Indicates how concentrated or dispersed data points are.

Understanding variability helps in assessing predictability and consistency within your dataset—important when making inferences about population trends.

Outliers

Outliers are data points that deviate significantly from the rest of the dataset. They can occur due to variations in measurement, sampling errors, or naturally present extremes. When using a stemplot, outliers are noticeable as leaves that lie far away from the cluster of other values.

To identify outliers:

• Check for leaves or data points that stand alone or are distant from the rest.
• Consider whether these points are due to recording errors or true variations.

Identifying outliers is crucial as they can disproportionately affect statistical measures such as the mean, variance, and skewness, potentially misleading analysis and conclusions.