Question

Agronomists measured the yield of a variety of hybrid corn in 16 locations in Illinois. The data, in bushels per acre, were \(^{17}\) \(\begin{array}{llllll}241 & 230 & 207 & 219 & 266 & 167 \\ 204 & 144 & 178 & 158 & 153 & \\ 187 & 181 & 196 & 149 & 183 & \end{array}\) (a) Construct a dotplot of the data. (b) Describe the shape of the distribution.

Short answer

A dotplot is constructed by listing the data in order, creating a horizontal scale, plotting the points, and then the shape of the distribution is described based on the visual representation of the data.

Step-by-step solution

List the Data in Ascending Order

Before constructing the dotplot, organize the data in ascending order to make the plotting process easier. Sort all the provided data from the smallest to the largest value.

Draw a Horizontal Scale

Draw a horizontal line and mark a scale on it that includes the smallest and largest data values. The scale should have increments that allow for all values in the data set to be plotted.

Plot the Data Points

Above each number on the horizontal scale, place a dot for each time that number of bushels per acre occurs in the data set. If more than one occurrence of a data point happens, stack the dots vertically.

Complete the Dotplot

Review the dotplot to make sure all data values are represented correctly. Label the axes with appropriate titles, such as 'Bushels per Acre' for the horizontal axis.

Describe the Shape of the Distribution

By observing the dotplot, describe the distribution of the data in terms of its shape (e.g., symmetric, skewed left or right, uniform) and note any apparent outliers or clusters of data.

Key concepts

Descriptive Statistics

Descriptive statistics involve summarizing and organizing data so that it can be easily understood. Common descriptors include measures of central tendency like mean, median, and mode, as well as measures of variability like range, variance, and standard deviation. For agronomists analyzing corn yields, these statistics provide insight into the average performance, consistency, and variability of the crops. By listing data in ascending order before constructing a dotplot, as mentioned in our example, the agronomists make the subsequent steps of analysis more manageable. Understanding these basic statistics is crucial when analyzing agronomic data, as it lays the groundwork for making informed decisions about agricultural practices and crop selection.

When applying descriptive statistics to the corn yield data, for instance, they would calculate the average yield, identify the highest and lowest yields (the range), and assess how much variability exists within the yields, which could influence future plantings or research into certain hybrid crops.

Data Visualization

Data visualization is a powerful tool for conveying information about data through graphical representations. A dotplot, like the one constructed from the Illinois corn yield data, is a simple yet effective form of data visualization. It helps in quickly understanding the distribution of data points without complex calculations or in-depth statistical knowledge. The visual representation provided by a dotplot can reveal trends, patterns, and outliers that might not be apparent from the raw data alone. The key to a useful dotplot is an accurate scale and clear labelling, ensuring the data tells a meaningful story. For students and researchers alike, mastering the creation and interpretation of data visualizations like dotplots is essential in fields where making sense of large datasets is a part of the analysis process.

Distribution Shape Analysis

Understanding the shape of a data distribution is a vital part of descriptive statistics and is particularly useful in identifying patterns and anomalies. Distributions can be symmetric, skewed left or right, or uniform among other shapes. In the context of the agronomic data analysis, the shape can indicate the overall performance and the consistency of the yields across different locations. Analyzing the shape can help determine if the data follows a normal distribution, which is often an assumption in further statistical testing. By creating a dotplot, it becomes easier to visualize and describe the distribution's shape. For example, a dotplot with most data points clustered to the left and the rest trailing off to the right suggests a right-skewed distribution, possibly indicating a few locations with exceptionally high yields that might warrant further investigation.

Agronomic Data Analysis

Agronomic data analysis involves the application of statistical methods to agricultural data to improve crop production and maintenance. Gathering data like corn yield from different locations, as in the exercise, can help agronomists detect variations in crop performance due to geographical differences, climate conditions, soil quality, or other agronomic factors. The analysis of this data can inform decisions about where to focus resources or how to manage crops for better yields. The dotplot provides a quick visual overview that can highlight areas needing attention, such as locations with significantly lower yields. This type of analysis is critical for sustainable farming practices and maximizing productivity within the agricultural industry.