20.8 Statistics

This activity is from the Sourcebook for Teaching Science.

• IntroductionWhat is the difference between linear, polynomial and exponential functions?

• Use Desmos to plot linear, polynomial and exponential functions.

• What is a best fit?

• What is the meaning of R2? 

Best Fit

Obtain the best fit equations for the following using 

• • Spreadsheet for 20.8 Statistics on air quality (20.8.1)

  • Car acceleration in 20.8.2

  • Pendulums in 20.8.1

  • Relationship of Temperature and pressure in gases 

  • Relationship of atmospheric carbon dioxide to time

Activity 20.8.1 – Descriptive statistics: Making sense of the data

In 1952, a sulfur-laden smog covered London, England, leading to the deaths of approximately 4000 people.  In 1963 an air pollution inversion occurred in New York City, leading to 168 deaths.  Shocking tragedies such as these lead to the passage of the Air Quality Control Act in the United States, and similar measures in other parts of the world.  Since the passage of this landmark act in 1967, agencies have been commissioned to measure pollution and set standards.  

Figure 20.30[i] shows the number of “unhealthful air” days per year in some of the major cities in America in 1999. To determine the percentage of days that are considered to have “unhealthful air”, divide the number of unhealthy days by 365 days per year and convert to percent.  Once the formula has been entered in the top cell, it can be copied to the remaining cells. When you have completed this calculation, determine the average  (=AVERAGE(first cell: last cell)) and median (=MEDIAN(first cell: last cell))  number of unhealthful days for the cities listed.  Finally, determine the city with the largest number of unhealthful days (=MAX(first cell: last cell)) and the city with the least (=MIN(first cell: last cell)).

Activity 20.8.2 – Trendlines: Discovering relationships in the data

A trendline is a best-fit line through a series of data points.  A trendline can be a linear, exponential, power, logarithmic, or polynomial function. Trendlines help researchers visualize relationships.  The best trendline is the one that best fits the data.

(1) Motion  – Table 20.7A lists time and distance data for an accelerating automobile. Graph this data and determine the best trendline. Try all types to see which fits the data best.

(2) Pendulums – In 1656, Christian Huygens, a Dutch scientist, invented the first pendulum clock.  What formulas govern the movement of pendulums?  Plot the experimental data from table 20.7B and determine the best trendline.  Is the relationship linear, exponential, power, logarithmic, or polynomial .  What is the basic equation of the pendulum?