Question

An Archeological Find An article in Archaeometry involved an analysis of 26 samples of Romano-British pottery, found at four different kiln sites in the United Kingdom. \({ }^{16}\) The samples were analyzed to determine their chemical composition, and the percentage of aluminum oxide in each of the 26 samples is shown in the following table. a. Construct a relative frequency histogram to describe the aluminum oxide content in the 26 pottery samples. b. What unusual feature do you see in this graph? Can you think of an explanation for this feature? c. Draw a dotplot for the data, using a letter (L, C, I, or A) to locate the data point on the horizontal scale. Does this help explain the unusual feature in part b?

Short answer

Answer: The main purpose of creating a dotplot after constructing a relative frequency histogram is to reveal additional patterns and relationships in the data that might help explain any unusual features observed in the histogram, by showing the relationship between different variables or categories, such as the kiln sites and the percentage of aluminum oxide in the pottery samples.

Step-by-step solution

Compute the relative frequency for each data value

To find the relative frequency, we'll first count the number of times a range of values appears in the dataset. Then we'll divide that count by the total number of samples (26). Recall that a histogram breaks the range of values into intervals or bins. You can choose the number of bins and the width of each bin according to your preference, but we recommend using 5-10 intervals for this problem.

Create the histogram with bins and relative frequency

Once you have computed the relative frequencies, create the histogram. On the horizontal axis, place the intervals (bins) you determined in Step 1. On the vertical axis, plot the relative frequency of each bin. Use bars to represent the frequency of each bin. Make sure the bars touch each other, as there should be no gaps between them in a histogram.

Analyze the histogram and identify unusual features

Examine the histogram and look for any unusual features. This section will require interpretation, as the unusual feature(s) you identify will depend on the dataset. Unusual features can include gaps, clusters, peaks, or any other unexpected patterns in the data.

Explain the unusual feature

After identifying the unusual feature, try to come up with a possible explanation for the feature. This explanation might involve doing additional research on the composition or historical context of Romano-British pottery samples.

Create a dotplot with labeled data points

Draw the dotplot by placing points on the horizontal scale, which represents the percentage of aluminum oxide. Label each data point with the corresponding letter L, C, I, or A (for each of the four different kiln sites). The dotplot allows you to see the same data differently and might give insights into the unusual feature seen in the histogram.

Interpret the dotplot

Look at the dotplot and try to correlate the labeled data points with the unusual feature found in the histogram. The dotplot can reveal patterns that might explain the unusual feature by showing the relationship between the kiln sites and the percentage of aluminum oxide in the samples. Determine if the dotplot helps to explain the unusual feature you found in the histogram.

Key concepts

Relative Frequency Histogram

A relative frequency histogram is a visual tool in statistics that depicts the relative frequency of data points within specified ranges, known as bins, for a dataset. Relative frequency is calculated by dividing the count of data points in a bin by the total number of data points. To create a relative frequency histogram, such as for the archaeological analysis of Romano-British pottery, one must first determine the range of data to compute the intervals.

For instance, if the data shows the percentage of aluminum oxide in pottery samples, each bin might represent a range of percentages. The height of the bars in the histogram then illustrates how frequently data within each percentage range occurs relative to the whole data set. This type of histogram allows archaeologists—or students—to quickly see the distribution of chemical composition across samples and identify commonalities or anomalies within the data.

To ensure clarity in the histogram, it's essential that the intervals are chosen appropriately. An overly large number of bins might complicate the histogram with too much detail, while too few may oversimplify the data and obscure important features. As detailed in the step-by-step solution, there should be no gaps between bars in a well-constructed histogram, ensuring a continuous representation of data without implying any intervals devoid of data.

Chemical Composition Analysis

Chemical composition analysis is the process of identifying and quantifying the elements and compounds present within a material. In the context of archeology, analyzing the chemical composition of artifacts like pottery can provide insight into the resources and technologies used by ancient cultures. The noted analysis of Romano-British pottery involves examining the aluminum oxide content in different samples, which could indicate the type of clay used or the firing techniques employed at various kiln sites.

To analyze the chemical composition effectively, scientists use various techniques, including spectroscopy, chromatography, and microscopy. The gathered data then contributes to understanding the technical capabilities and trade networks of historical populations. For students encountering this exercise, recognizing the importance of analyzing chemical composition deepens their appreciation for how modern scientific techniques are applied to study the past and draw conclusions about historical practices. It also underscores the relevance of accurately presented data in guiding scientific and historical interpretations.

Data Interpretation in Statistics

Data interpretation in statistics involves extracting meaning from numerical information, which often requires recognizing patterns, anomalies, or trends within a dataset. When analyzing Romano-British pottery, for example, students need to not only build histograms and dotplots but also discern what these visual tools reveal about the artifact's history or production.

The recognition of an unusual feature in the histogram, such as an unexpected peak or gap, prompts further investigation and interpretation. A gap might denote a lack of pottery with certain chemical properties, while a peak could indicate a preferred composition. In turn, these observations could lead to hypotheses about cultural practices, resource availability, or production methods.

By interpreting these features, students learn to draw conclusions from data—an essential skill in both archeological research and broader scientific inquiry. It is crucial that students understand the relationship between data visualization, such as histograms and dotplots, and the conclusions that can be drawn from them. This ensures a well-rounded approach to statistical analysis, empowering students to make informed interpretations of data within its real-world context.