Graphical Analysis In Exercises 9–12, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer.

Verified step by step guidance

1. Observe the histogram provided. Note the distribution of frequencies across the bins, which represent ranges of values (e.g., 25,000 to 85,000).
2. Identify the general trend of the bars. In this histogram, the bars are tallest on the left side and gradually decrease in height as you move to the right.
3. Understand the concept of skewness. A distribution is skewed right if the tail extends to the right (towards higher values) and skewed left if the tail extends to the left (towards lower values). Symmetric distributions have equal tails on both sides, and uniform distributions have bars of roughly equal height.
4. Compare the histogram's shape to these definitions. The histogram shows a long tail extending to the right, indicating that the distribution is skewed right.
5. Justify the conclusion: The majority of the data is concentrated on the lower end (left side), with fewer occurrences as the values increase, which is characteristic of a right-skewed distribution.

Key Concepts

Histogram

A histogram is a graphical representation of the distribution of numerical data, where the data is divided into intervals (bins) and the frequency of data points within each interval is represented by the height of bars. It helps visualize the shape of the data distribution, making it easier to identify patterns such as symmetry, skewness, and modality.

Distribution Shape

The shape of a distribution refers to the way data points are spread across the range of values. Common shapes include symmetric (equal on both sides), uniform (equal frequency across intervals), skewed left (tail on the left), and skewed right (tail on the right). Understanding the shape is crucial for interpreting data characteristics and making statistical inferences.

Skewness

Skewness measures the asymmetry of a distribution. A distribution is skewed left if it has a longer tail on the left side, indicating that most data points are concentrated on the right. Conversely, a skewed right distribution has a longer tail on the right side. Identifying skewness helps in understanding the underlying data trends and potential outliers.