1. Describe the field of statistics, and state the meaning of the term descriptive statistics.
2. Explain what elements, variables, and observations are.
3. Describe the difference between qualitative and quantitative variables, and between discrete and continuous variables.
4. State the four levels of measurement.
5. Describe what is meant by a population, a sample, a parameter, and a statistic, and explain statistical inference.

• collecting data
• analyzing data
• presenting data
• interpreting data

• Phase 1 Data collection. The first phase of a statistical study, as in the definition of statistics, is to collect the data. The researchers obtained data kept by the British Department of Transport on the traffic flow through certain junctions of the M25 motorway in England.
• Phase 2 Data analysis. Next is the analysis of the data. The authors compared the number of vehicles passing through certain junctions on the M25 motorway on Friday the 13th and the previous Friday.
  Table 1.2: Table 2 Traffic through M25 junctions

  Friday the 6th	Friday the 13th	Difference
  139,246	138,548	698
  134,012	132,908	1104
  137,055	136,018	1037
  133,732	131,843	1889
  123,552	121,641	1911
  121,139	118,723	2416
  128,293	125,532	2761
  124,631	120,249	4382
  124,609	122,770	1839
  117,584	117,263	321

  fridaythe13th

  Table 2 shows that, in every instance, the number of vehicles passing through these junctions on Friday the 13th was less than on the preceding Friday. Now, let's examine the data graphically. The clustered bar graph in Figure 4 illustrates the difference in the number of vehicles traveling on the M25 motorway on Friday the 6th (in green) and the subsequent Friday the 13th (in yellow) for 10 pairs (clusters) of dates. Note that, in every instance, the green bar is longer than its partner yellow bar. This indicates that the number of vehicles on the motorway decreased on Friday the 13th when compared with the previous Friday in every instance.

  

  Figure 1.4: FIGURE 4 Clustered bar graph of motorway traffic.

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• Phase 3 Data presentation. The presentation of the results is important, and the researchers found a highly respectable journal, the British Medical Journal, in which to publish their findings. Other avenues for presentation are delivering a talk at a conference, writing up a report for one's supervisor, or presenting a class project.
• Phase 4 Data interpretation. Finally, the last facet in our definition of statistics is interpretation. It is crucial for those who are performing a statistical study to make their results understandable to the general public. It is not sufficient for the statistician alone to understand the results. Instead, the statistician must communicate the results clearly, whether in writing or orally. In this case, the researchers chose the decrease in number of vehicles as the criterion on which to base support for their hypothesis that people changed their behavior on Friday the 13th. Their finding of an observable decrease in traffic on Friday the 13th is consistent with their hypothesis.

YOUR TURN #1

1. List the values that the variable type takes.
2. Provide the observation for Spiderman 2 for PS4.

Not all numerical variables are quantitative. For example, a zip code such as 90210 is numerical. But we would not perform arithmetic on zip codes, such as adding two zip codes together. Therefore, zip codes are numerical but not quantitative.

NASDAQ is an American stock exchange that includes many technology companies.

1. The elements are the five most active stocks traded on the NYSE and NASDAQ on this day in 2014. The variables are as follows:
   • Exchange: the exchange where the stock was traded.
   • Last: the most recent trading price for the stock.
   • Volume: how many shares of the stock were traded that day.
   • Change: the change in share price (in dollars) between the opening price and the closing price that day.
2. The exchange, because it can be categorized as either NYSE or NASDAQ, is qualitative. The other variables are quantitative.
3. The observation for Bank of America includes the exchange and the set of the day's stock data for that company. Bank of America is traded on the NYSE. Its last share price was $15.21 per share, 48,690,356 shares of its stock were traded, and the price decreased by $0.05 per share.

YOUR TURN #2

1. Is Sirius XM an element or a variable?
2. What is another term for the variable Exchange?

Hint: A quantitative variable that must be counted (not measured) is probably a discrete variable, whereas a quantitative variable that must be measured (not counted) is probably a continuous variable.

1. Because the number of math courses is finite, the variable number of math courses taken is discrete.
2. Because GPA can take an infinite number of possible values (for example, in the interval 0.0 to 4.0), the variable GPA is continuous.

YOUR TURN #3

1. Number of medals won.
2. Racing time in the 100-meter dash.

1. Years covered in European History 101: 1066–1492
2. Annual income of students in Statistics 101 class: $0–$15,000
3. Course grades in English 101: A, B, C, D, F
4. Student gender: male, female

1. The years 1066 to 1492 represent interval data. No natural zero occurs (no “year zero”; the calendar goes from 1 b.c. to a.d. 1). Also, division () does not make sense in terms of years, so that the data are not ratio data. However, subtraction does make sense, in that the course covers .
2. Student income represents ratio data. Here, division does make sense. That is, someone who made $4000 last year made twice as much as someone who made $2000 last year. Also, some students probably had no income last year, so that $0, the natural zero, also makes sense.
3. Course grades represent ordinal data, because (a) they may be arranged in a particular order, and (b) arithmetic cannot be performed on them. The quantity A 2 B makes no sense.
4. Student gender represents nominal data, because the data cannot be ordered in a natural or obvious way. Also, no arithmetic can be performed on student gender.

YOUR TURN #4

1. Exchange
2. Last price

1. The seven continents: Asia, Africa, North America, South America, Europe, Antarctica, Australia
2. Europe and North America
3. All of Ludwig van Beethoven's nine symphonies
4. Beethoven's 5th, 6th, and 9th symphonies

1. Because all of the continents are listed, this group represents a population.
2. Europe and North America represent a subset of the population of all continents and, therefore, represent a sample.
3. Because all of Beethoven's symphonies are included, this represents a population.
4. Because the 5th, 6th, and 9th symphonies represent a subset of all of Beethoven's symphonies, this is a sample.

YOUR TURN #5

1. The three largest counties in Florida.
2. All of the counties in Florida.

1. The average income of the countries in all seven continents
2. The average income of the countries in Europe and North America
3. The shortest (in time) of all of Beethoven's nine symphonies
4. The shortest (in time) of Beethoven's 5th, 6th, and 9th symphonies

1. Because all seven continents represent a population, the average income is a parameter.
2. Only two of the seven continents are represented, so the average income of this sample is a statistic.
3. Since all of Beethoven's nine symphonies represent a population, the shortest time is a parameter.
4. Only three of the nine symphonies are represented, so the shortest time of this sample is a statistic.

YOUR TURN #6

1. The most expensive hotel in the three largest counties in Florida
2. The most expensive hotel in all of Florida (that is, all of the counties in Florida)

1. In Baltimore County, Maryland, the average amount spent per week on gasoline consumption in a sample of 500 commuters was $75. The county government infers that the average amount spent weekly by all Baltimore County commuters is $75.
2. A sample of 100 residents of Broward County, Florida, yielded 27 residents who work for the government at the local, state, or federal level. Thus, 27% of these 100 residents work for the government.
3. The average age of a sample of 200 residents of Garden City, New York, was 34 years old.
4. In a survey of 1000 citizens in the Seattle, Washington, metropolitan area, 570 said they would pay higher prices in order to reduce greenhouse emissions. City planners conclude that 57% of all Seattle citizens would do so.

1. Statistical inference. A sample was taken, and a sample statistic ($75 per week) was calculated. Then the county government used this statistic to make the statistical inference that this was the average amount spent by all Baltimore County commuters.
2. Descriptive statistics. Though a sample was taken, there was no attempt to make an inference from this sample of 100 workers to the entire population of Broward County, Florida. So, no statistical inference is being made here.
3. Descriptive statistics. The average age of 34 years old is a descriptive statistic, because it describes the sample. However, no inference is made regarding a larger population.
4. Statistical inference. The survey found that 57% of the sample of 1000 citizens would pay higher prices in order to reduce greenhouse emissions. This 57% is a statistic. Then the city planners used this statistic in order to perform statistical inference about the population of all Seattle citizens.

YOUR TURN #7

1. Your instructor states that the average grade on the first quiz for your class is 85.
2. In 10 games of ping pong, Jessica has lost to her friend Lu Li 8 times. Jessica sadly concludes that, going forward, she has only a 20% chance of winning a game of ping pong against her friend Lu Li.

1. A fair coin is tossed five times and comes up heads each time. That means that tails is “due” and the chances of tails on the next toss is increased.
2. One politician says that the mean income is rising, whereas another politician says that the median income is falling. One of them has to be lying.
3. Jim is tested for HIV and the test comes back positive. Thus, Jim is HIV-positive.