Common Core Math I Unit 1: One-Variable Statistics Comparing Data Sets

Comparing Two Sets of Data Do boys have better balance than girls? How can we answer this question? What experiment can we do? What would we measure?

Balancing on One Foot Group Roles: timer, recorder, balancer (rotate roles until each person has had a chance to balance on one foot) Follow this procedure: Comfortably balance on your dominant foot before closing your eyes. Timing starts when you close your eyes and say “start”. Time ends when you: Put your other foot down Open your eyes Touch an object for balance with hand or foot Balance for more than 3 minutes Record your time. Collect your group’s data on a post-it note and bring to the front – be sure to list which values are male and which are female. Put students in groups of 3. The students can wiggle, but not hop or spin while balancing. Write data on the board and have students enter into List1 and List2 on the calculator.

Side-by-Side Boxplots Using technology, create side-by-side boxplots. Show students how to create side-by-side boxplots in the calculator (set up Plot1 to graph the data in List1 and Plot2 to graph the data in List2 and turn both “ON”). Have them transfer sketches of the box plots to graph paper, using a single number line scale. Be sure to label which box plot is male and which is female.

Creating Histograms Using technology, create a histogram of each set of data. Make sure you use the same scale for each! Show students how to create histograms using the same window (that works for both graphs) on the calculator. Have them transfer sketches of the histograms to graph paper. Be sure to label which box plot is male and which is female.

Comparing The Data Sets Write a description comparing the two data sets in context. Address shape, center, spread, and outliers. Answer the question, “Who balances better?” Which representation gives you more information? Which numerical measures best describe the data sets? Explain. Have students do this with their groups. Share out and discuss.

Comparing Types of Peanut Butter Have students complete the Comparing Data Sets Practice activity in pairs or groups. Discuss answers. Have a couple of groups share their descriptions and discuss the quality of their narratives. The rest of class time can be spent on the Poster Project.

Comparing Types of Peanut Butter Natural Regular Statistic Natural Peanut Butter Regular Peanut Butter Min 34 11 Q1 57 31 M 61.5 40 Q3 69 54 Max 89 83 IQR 12 23 mean 61.2 42.7 standard deviation 13.6 18.8 Natural Peanut Butter Outliers: 34, 89 Which measure of center and spread would be most appropriate to use to describe these two sets of data? Explain. It would be most appropriate to use the median and the IQR since the Natural Peanut Butter Quality Ratings data set has outliers. Note that since there are outliers on both ends of the data set, they balance out their effects on the mean and thus the value of the mean, 61.2, is close to the value of the median, 61.5. However, the outliers do inflate the value of the standard deviation, 13.6, as compared to the IQR of 12.   Compare the two data sets in context. Be sure to address shape, center, spread, and outliers. Which type of peanut butter is better? The distribution of quality ratings for natural peanut butter is slightly skewed to the left as evidenced by the longer whisker on the left side of the box. The distribution of the quality ratings for regular peanut butter is fairly symmetrical. Natural peanut butter has higher quality ratings than regular peanut butter with a median of 61.5 points for natural vs. 40 points for regular. The ratings for regular peanut butter are more spread out, ranging from 11 points to 83 points, and therefore less consistent than the ratings for natural peanut butter which ranges from 34 to 89 points. This can also be seen in the spread of the middle 50% of the data: the spread of the middle for regular peanut butter is 23 points but the spread of the middle for natural peanut butter is 12 points. Overall, natural peanut butter has higher quality ratings.