Calculate, use, and interpret the mean, median, mode, range for a set
Part I: Mean, Median, Mode, & Range
Objective
• Calculate, use, and interpret the mean, median, mode, range for a set of data.
Activity
Have the students find the mean yearly gas prices from 1976-2005 and write their answers in the column named “Annual Mean.” Have the students do the attached worksheet titled “Mean, Median, Mode, & Range.” You can also have the students create various lists by looking at certain months or a select group of years and analyze the mean or median of each individual month or the median of each year. Teach the students how to use the “SortA(“ and “SortD(“ functions on the calculator to rearrange the data in either ascending or descending order so that they can more easily find the range and modes.
Assessment
Students will be graded not only on mathematical computations but also on their analysis of interpretation questions written in short answer form.
Part II: Scatter Plots & Linear Regression
Objective
• Collect, organize, analyze, and display data (including scatterplots) to solve problems.
• Approximate a line of best fit for a given scatterplot; explain the meaning of the line as it relates to the problem and make predictions.
Activity
Have students look back at their answers in the “Annual” box beside each year. If you did not do the Part I activity then you can give them Table 2 which includes the needed information. Have the students create a table in either a graphing calculator or a computer program so that when a scatter plot is graphed, the years are on the x-axis and the annual mean is on the y-axis. Instruct each student to look at the scatter plot and determine if they can visual see any pattern or a positive or negative regression line. Then have the students actually plot the linear regression line that best fits the data and determine the projected cost of gas will be in the year 2030 and explain why they feel this may or may not be a good prediction.
Assessment
Students will be graded on their data plots and on their linear regression line. They will also be graded on their use of this data to predict and analysis of results. Finally the students will be graded on their group project which will be presented to the class.
Part III: Box Plots
Objective
• Collect, organize, analyze, and display data (including box plots) to solve problems.
• Calculate, use, and interpret the inter-quartile range for a set of data.
• Identify outliers and determine their effect on the a set of data.
Activity
Take the list of average annual gas prices (either from Table 2 or the chart they received and filled out in Part I) and create a box plot. The students can then trace the box plot to find the minimum, quartile 1, median, quartile 3, and maximum values. From here, have the students find the interquartile range, find outliers and then analyze whether there is bad data and if the scatter plot produces an even distribution or if the graph is skewed.
Assessment
Students will be graded on finding the key points of a box plot graph and their written description of the analysis of results with respect to good and bad data. Finally, the students will be graded on their group project that will be presented to the class.
Part IV: Scatter Plot & Median-Median Line
Objective
• Collect, organize, analyze, and display data (including scatterplots) to solve problems.
• Find the median-median line for a given scatterplot; explain the meaning of the line as it relates to the problem and make predictions.
• Compare two different types of regression lines and which is more accurate for the data.
Activity
The students create a scatter plot putting the years on the x-axis and the annual means on the y-axis and find a median-median line which could be a more consistent regression line. Using the median-median line, they can find the residuals and the root mean square error of the data. They can then use this information to extrapolate data. They should also create a line of best fit and explore the differences between the line of best fit and the median-median line and determine which is actually a more accurate line for the data.
Assessment
Students will be graded on the median-median line and the standard deviation. They will also be graded on their analysis of what the data means and their comparison of the two types of linear regression lines and their prediction of possible future gas prices.
