Question

Starbucks The number of Starbucks coffee shops in cities within 20 miles of the University of California, Riverside is shown in the following table. \({ }^{20}\) a. Draw a dotplot to describe the data. b. Describe the shape of the distribution. c. Is there another variable that you could measure that might help to explain why some cities have more Starbucks than others? Explain.

Short answer

a. Draw a dotplot to describe the data. * * * * * * * * * * * * * * ___________ 1 2 3 4 5 6 b. Describe the shape of the distribution. The dotplot created shows a distribution that is unimodal, with its highest peak at City 4. The distribution is slightly skewed to the right, indicating that there may be more cities with a higher number of Starbucks stores than those with fewer. There are no significant gaps or clusters in the data; the points are relatively evenly dispersed along the horizontal axis. c. Suggest another variable that might help explain why some cities have more Starbucks than others. Considering the context of the data given, college or university presence might be a relevant variable to help explain the distribution. The University of California, Riverside, could attract a higher number of Starbucks due to the concentrated student population in the area. Additionally, other nearby college or university campuses could contribute to the demand for Starbucks coffee shops in the cities surrounding the University of California, Riverside.

Step-by-step solution

Create a dotplot

In order to create a dotplot, you need to plot each data point as a dot on a horizontal line. The data points should be aligned vertically, and there should be a higher dot for every additional Starbucks location in a city. You should create a dotplot following the guidelines mentioned above. Make sure each dot is clearly visible and properly corresponds to the number of Starbucks in the city.

Describe the shape of the distribution

After creating the dotplot, you need to observe its shape and describe it in words. Look for any patterns that might emerge, such as: - Symmetry: Is the distribution symmetrical, meaning it has roughly the same number of points on both sides of its center? Or is it skewed, meaning it has more points on one side than the other? - Peaks: Does the distribution have a single peak (unimodal) or multiple peaks (bimodal, multimodal)? Which area has the peak? - Gaps: Are there any noticeable gaps or clusters within your dotplot? Once you have observed these characteristics, write a few sentences describing the distribution's shape.

Consider other variables that could help explain the distribution

Now we need to think about potential factors that could affect the number of Starbucks in a city. Some possible variables to consider are: - Population: Cities with higher populations might have more Starbucks coffee shops. - College/university presence: Cities with colleges or universities might have more Starbucks due to the student population. - Business districts: Cities with large business districts may have more Starbucks as they cater to working professionals. - Tourism: Tourist destinations might have more Starbucks to cater to the influx of visitors. Based on these possible variables, consider which one(s) might be relevant in the context of the data provided and explain your reasoning.

Key concepts

Dotplot Creation

Understanding the distribution of data points is vital in statistical data analysis, and creating a dotplot is a fundamental skill for visualizing this information. To create a dotplot, start by drawing a horizontal line that represents the scale of your data. Each city's Starbucks count is represented by a dot placed above the corresponding number on your scale.

For example, if a city has one Starbucks, you place one dot above the number one on your line. If another city has four Starbucks, you stack four dots above the number four. It's important to ensure that dots representing the same value are directly aligned above one another to accurately depict the frequency. Clear labeling is also crucial in a dotplot, so don't forget to include a title that reflects what the data represents and label your axes appropriately. The simplicity of a dotplot makes it an excellent tool for quickly recognizing patterns or outliers in small sets of data.

Distribution Shape Description

After creating a dotplot, the next step is to describe the shape of the distribution it represents. This involves looking at the overall outline formed by the dots and noting features such as symmetry, whether it's skewed to the left or right, and the number of peaks.

A symmetrical distribution suggests a balance on both sides, while a skewed distribution implies that one tail is longer than the other. Peaks in a distribution indicate where data points are concentrated; a single peak denotes a unimodal distribution, whereas multiple peaks suggest a bimodal or multimodal distribution. In addition to peaks, it's crucial to identify gaps or clusters which could be indicative of distinct groups within the data set or potential outliers. Describing these features in a distribution helps provide a narrative for what the data may be indicating, offering insights at a glance.

Statistical Data Analysis

In the realm of statistical data analysis, looking beyond the primary data we collect is essential to understand the underlying causes of observed patterns. In the case of the number of Starbucks in various cities, exploring other variables may shed light on the distribution presented in the dotplot.

For example, population size is a common variable that can be considered to explain the density of Starbucks outlets. A larger population often means a greater demand for coffee shops. Additionally, the presence of a university or college can influence the number of Starbucks due to a higher density of students and faculty who may prefer such establishments. A bustling business district may also correlate with a higher number of Starbucks due to the demand from working professionals. Lastly, cities that are popular tourist destinations could have more Starbucks to cater to the needs of visitors.

Exploring these variables can not only help explain existing patterns but also assist in predictive analysis for future business decisions such as the placement of new coffee shops. A thorough investigation into these additional factors is pivotal in drawing more nuanced conclusions from the data.