Question

How safe is your neighborhood? Are there any hazardous waste sites nearby? The table and the stem and leaf plot show the number of hazardous waste sites in each of the 50 states and the District of Columbia in \(2016 .^{5}\) \(\begin{array}{lrlrlrlrlr}\text { AL } & 15 & \text { HI } & 3 & \text { MA } & 33 & \text { NM } & 16 & \text { SD } & 2 \\ \text { AK } & 6 & \text { ID } & 9 & \text { MI } & 67 & \text { NY } & 87 & \text { TN } & 17 \\ \text { AZ } & 9 & \text { IL } & 49 & \text { MN } & 25 & \text { NC } & 39 & \text { TX } & 53 \\ \text { AR } & 9 & \text { IN } & 40 & \text { MS } & 9 & \text { ND } & 0 & \text { UT } & 18 \\ \text { CA } & 99 & \text { IA } & 13 & \text { MO } & 33 & \text { OH } & 43 & \text { VT } & 12 \\ \text { CO } & 21 & \text { KS } & 13 & \text { MT } & 19 & \text { OK } & 8 & \text { VA } & 31 \\ \text { CT } & 15 & \text { KY } & 13 & \text { NE } & 16 & \text { OR } & 14 & \text { WA } & 51 \\ \text { DE } & 14 & \text { LA } & 15 & \text { NV } & 1 & \text { PA } & 97 & \text { WV } & 10 \\ \text { DC } & 1 & \text { ME } & 13 & \text { NH } & 21 & \text { RI } & 12 & \text { WI } & 38 \\\ \text { FL } & 54 & \text { MD } & 21 & \text { N } & 115 & \text { SC } & 25 & \text { WY } & 2 \\ \text { GA } & 17 & & & & & & & & \end{array}\) a. Describe the shape of the distribution. Identify the unusually large measurements marked "HI" by state. b. Can you think of a reason why these states would have a large number of hazardous waste sites? What other variable might you measure to help explain why the data behave as they do?

Short answer

Question: Based on the given data and analysis, a) describe the shape of the distribution and identify states with unusually high amounts of hazardous waste sites, and b) propose a reason why these states would have a large number of hazardous waste sites and suggest another variable to measure to help explain the data.

Step-by-step solution

Observing the Data

Read through the given information and note the number of hazardous waste sites in each state. Compare these numbers and identify any patterns or trends in the data.

Distribution Shape

After observing the data, describe the overall shape of the distribution. Is it skewed (and if so, in which direction), or is it roughly symmetrical?

Identify Unusually High Measurements

Look for any states with significantly higher numbers of hazardous waste sites than most other states. These would be considered as unusually high measurements and should be marked "HI" according to the instructions. b) Reason for High Number of Hazardous Waste Sites and Suggesting Another Variable

Analyze and Reason

Using the identified states with unusually high measurements and the given context, analyze what factors could be contributing to their high number of hazardous waste sites. This may require additional research or just an understanding of economic, geographic, or population-based factors of those states.

Suggest Another Variable

Based on your analysis and reasoning, propose another variable that might be measured to help explain the behavior of the data. Consider factors such as population density, industrial development, geographical location, or economic conditions, among others.

Key concepts

Data Distribution Analysis

Understanding the distribution of data is essential when dealing with large datasets such as those detailing the number of hazardous waste sites across different regions. By analyzing the distribution, we can ascertain the overall pattern and identify any deviations from the norm. A dataset may be symmetrical, where the data points are evenly distributed on both sides of the average, or skewed, indicating that the data tends to fall more towards one side of the scale.

In the context of environmental statistics, a skewed distribution may point to a concentration of hazardous waste sites in certain areas due to factors such as industrialization levels or population density. To ease the interpretation, visual aids like stem-and-leaf plots or histograms can be used to better illustrate the shape of the data distribution. This graphical representation empowers learners with a clear visual of data spread, including any clumping of values or gaps, which are integral to understanding the environmental and health implications in different states.

Statistical Outliers

Statistical outliers are data points that differ significantly from the rest of the data. In the exercise dealing with hazardous waste sites, outliers can reflect states with an unusually high or low number of sites. Identifying these outliers is crucial as they can indicate anomalies that might be due to specific environmental policies, historical events, or economic factors.

However, not every outlier is a sign of a problem. Outliers can sometimes be the result of natural variation or unique conditions of a particular area. When teaching students about statistical outliers, it's important to instill a sense of caution about jumping to conclusions and encourage a thorough investigation of the potential reasons behind these anomalous data points before making any final assessments.

Environmental Data Interpretation

Interpreting environmental data involves looking beyond the numbers to understand the real-world implications of such statistics. It requires awareness of environmental science, policy, geography, and socio-economic conditions. When analyzing the number of hazardous waste sites, factors like the state's industrial history, regulatory framework, and environmental management practices come into play.

Moreover, additional variables, such as population density or economic status, might offer deeper insights into the 'why' behind the data patterns. For example, a densely populated state with a high GDP might have more hazardous waste sites due to more industrial activity. Teaching students to approach environmental data holistically ensures they not only comprehend the statistical information but also the broader context, enabling informed conclusions and actions.