Activity 1: Descriptive Statistics
Activity
The descriptive statistics discussed in this activity include:
The teacher should provide all students with the worksheet that accompanies the form of technology available. The worksheet includes a data set of 30 test scores for male students and 30 test scores of female students; step-by-step instructions for using each technology method; and guiding questions to help students determine whether boys or girls perform better.
Students begin by analyzing the data set and making an educated guess about which group performed better. They then use the technology to compare the mean and median of the data. To add more depth to the activity, the measures of center are very close. Thus, students should consider the variability of the data. Once they have done this, they will be able to come to a solid conclusion about the two groups.
Activity Rationale
The mathematical practice standards are met in various ways. Students must reason through the data set provided and the statistical data collected to determine who performed best on the test. They have to provide an argument as to why they believe one group performed better than the other. This argument must be supported by that statistics they collected. In doing all of this, they will use appropriate tools like calculators with statistics capabilities or an Excel spreadsheet.
Although it is important for students to understand what the mean, median, range, IQR, and standard deviation are and how they are calculated. It is not necessary that students always calculate these values by hand. With the advancements in technology, we are able to calculate all of these quicker and more easily than without. Not to mention, we are able to calculate these values for larger data sets. Even a concept as simple as the mean becomes tedious and burdening with a data set of 60 like we have.
CCGPS Standards Addressed
The descriptive statistics discussed in this activity include:
- Mean
- Median
- Range
- Inter-quartile range
- Standard deviation
The teacher should provide all students with the worksheet that accompanies the form of technology available. The worksheet includes a data set of 30 test scores for male students and 30 test scores of female students; step-by-step instructions for using each technology method; and guiding questions to help students determine whether boys or girls perform better.
Students begin by analyzing the data set and making an educated guess about which group performed better. They then use the technology to compare the mean and median of the data. To add more depth to the activity, the measures of center are very close. Thus, students should consider the variability of the data. Once they have done this, they will be able to come to a solid conclusion about the two groups.
Activity Rationale
The mathematical practice standards are met in various ways. Students must reason through the data set provided and the statistical data collected to determine who performed best on the test. They have to provide an argument as to why they believe one group performed better than the other. This argument must be supported by that statistics they collected. In doing all of this, they will use appropriate tools like calculators with statistics capabilities or an Excel spreadsheet.
Although it is important for students to understand what the mean, median, range, IQR, and standard deviation are and how they are calculated. It is not necessary that students always calculate these values by hand. With the advancements in technology, we are able to calculate all of these quicker and more easily than without. Not to mention, we are able to calculate these values for larger data sets. Even a concept as simple as the mean becomes tedious and burdening with a data set of 60 like we have.
CCGPS Standards Addressed
- Summarize numerical data sets in relation to their context
- Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
- Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
- Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Use appropriate tools strategically.
- Attend to precision.