MA.912.DP.5.11

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.912.DP.1.2 
• MA.912.DP.2.4
• MA.912.DP.2.8
• MA.912.DP.2.9 
• MA.912.DP.3.1
• MA.912.DP.3.2
• MA.912.DP.3.3
• MA.912.DP.3.4

Terms from the K-12 Glossary

• Data 
• Measures of center 
• Measures of variability 
• Population 
• Random sampling

Vertical Alignment

Previous Benchmarks

• MA.912.DP.1.1

Next Benchmarks

Purpose and Instructional Strategies

• Instruction includes the use of various media resources such as newspapers, magazines, internet, etc. Students should be able to identify whether a valid sampling method was used to collect data. Students do need to identify the type of sampling method, only if it is valid or if it creates bias. 
  • For example, if a sample is collected through a voluntary process, the sample is likely to contain more emotional or extreme responses. Participants who are not as passionate about the topic, are not as likely to take the time to respond. This could lead to a biased sample. 
• Instruction includes the exploration of misleading graphs and why they are misleading. Some types of misleading graphs are those that use a vertical axis that does not start at 0, uses inconsistent scales, uses different shapes or images instead of bars in bar charts, etc. Students should also discuss what the impact misleading graphs and data may have on society when they are allowed to be published as fact. 
• When looking at graphs that are misleading, students should have experience in deciding what can be done, if anything, to correct the presentation of the graph so that it is more accurate.

Common Misconceptions or Errors

• Students may not understand that there are alternative interpretations of data and statistics and that some may be biased. 
• Students may not be able to recognize survey questions that push participants towards a certain answer.

Instructional Tasks

• The manager of the Riverside Center is concerned about visitor numbers. He is certain the Center’s popularity has been badly affected by an increase in river pollution. He feels the local environmental agency should do something about it. To support his argument, he measured the chemical concentration in the river each month. He also counted the number of people visiting the Center over several months. He used the results to draw this chart. 
  Resource: Interpreting Data: Muddying the Waters 2015, MARS, Shell Center, University of Nottingham.
  
  
  

• At the same time the manager asked 18 visitors this question: ‘The odor you can smell originates from the pollution in the river. Is it spoiling your enjoyment of the Center?’ He displayed the results as a pie chart. 

• The Center Manager writes to the Environmental Officer to try to get something done about the river pollution:

• Part A. Describe in detail what you think the two charts show. 
• Part B. Do you think the Riverside Center Manager’s argument is fair? Explain your reasoning.

Instructional Items

• A local newspaper editor wants to determine the proportion of its readers who favor paying for improving local schools by increasing the property tax. Which technique would likely provide the most accurate, unbiased sample?
  a. The newspaper sends surveys to 1,000 subscribers at random.
  b. A reporter interviews 1,000 people walking along the street near the newspaper offices.
  c. Readers are asked to email the newspaper and express their opinion; 1,000 of these responses are selected at random.
  d. The editor selects 1,000 phone numbers at random from the phone directory covering the area. Each number is called and the respondents are interviewed.

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