Unit 1: Data collection Day 12: Do the Numbers Make Sense Note: “Pop” Summative Quiz at End of Class

What didn’t they tell us? Crested Butte attracts skiers by advertising that it has the highest average snowfall of any ski town in Colorado. News reports of snowstorms say things like “A winter storm spread snow across the area, causing 28 minor traffic accidents.” Eric Meyer, a reporter in Milwaukee, WI, called the sheriff to gather such numbers. Skiers want snow on the ski slopes, not in the town—and many other Colorado resorts get more snow on the slopes One day Meyer decided to ask the sheriff how many minor accidents are typical in good weather: about 48, said the sheriff. Perhaps, says Meyer, the news could say, “Today’s winter storm prevented 20 minor traffic accidents.”

Are the numbers consistent with each other? GM’s Cadillac brand was the best-selling luxury car in the US for 57 years in a row. In 1998, Ford’s Lincoln brand seemed to be winning until the last moment. Said the New York Times, “After reporting almost unbelievable sales results in December, Cadillac eked out a come-from-behind victory by just 222 cars.” Then GM reported that Cadillac sales dropped 38% in January. How could sales be so different in December and January? GM counted 4773 of its January sales as December sales

Are the numbers plausible? The very respectable journal Science, in an article on insects that attack plants, mentioned a California field that produces 750,000 melons per acre. Note: There are 43,560 square feet in an acre. 750000/43560=17.2 melons per square foot The editor had made a mistake. The correct figure was about 11,000 melons per acre. 11000/43560=.252525252525.... About 1 melon per 4 square feet.

Are the numbers too good to be true? In chemistry class, students are calculating the molar mass of a compound. One student’s lab report contains data that are exactly as the theory predicts. The teacher knows that the accuracy of the equipment and the student’s laboratory technique are not good enough to give such perfect results.

Is the arithmetic right? Australia’s Canberra Times reported, “Of those aged more than 60 living alone, 34% are women and only 15% are men.” An advertisement for a home security systems says, “When you go on vacation, burglars go to work. According to FBI statistics, over 26% of home burglaries take place between Memorial Day and Labor Day.” Where’s the other 51%? What might they have meant? Maybe: 34% of women over 60 live alone and 15% of men over 60 live alone This is supposed to convince us that burglars are more active in the summer vacation period. Look at your calendar. There are 14 weeks between Memorial Day and Labor Day. As a percent of the 52 weeks in the year, this is 14/52=.269 or over 26.9%

Unit 1 in summary The first and most important question to ask about any statistical study is “Where did the data come from?” The distinction between observational and experimental data is a key part of the answer. Good statistics starts with good designs for producing data. Then, we measure the characteristics of interest to obtain numbers we can work with. We should ask, “Do the numbers make sense?” It is a valuable habit to look skeptically at numbers before accepting what they seem to say.

Classroom Norms reminder Statisticians make mistakes Statisticians do not work alone There’s often more than one RIGHT answer (there are still WRONG answers too) In the end… you’ll get as much out of this class as you give Do not be afraid to share your work out of fear it might be wrong (Note: standards 2 and 3 are extensions of this rule) For a lot of our summative work you’ll be in groups…. If I notice a pattern of copying work from others, you’ll start working individually… If you miss class you will make up work with me… Reports will be unique All of your work will be unique but not always correct

Unit 1 Summative Part 1: Chance News Case Studies Exceeding Meeting Approaching Beginning Student thoughtfully answers each question with explanations when appropriate using reasoning skills. Student thoughtfully answers each question with explanations when appropriate but answers are incomplete or lack sufficient reasoning. Student answers most questions with explanations when appropriate. Student answers some questions with explanations when appropriate.