Warm-Up 4 87, 90, 95, 78, 75, 90, 92, 90, 80, 82, 77, 81, 95, 100 1. Find the 5-Number Summary for the data 2. Address every type of measure of spread. (range, standard deviation, and IQR)

HW Check from Tuesday and Wednesday night

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

Comparing Data Tuesday we looked at Johnny, Will, and Anna and compared their test scores. We only looked at their mean and standard deviation but when we have a larger set of data we need to look at a lot more to really get a good comparison.

Side-by-Side Boxplots One way is to compare is two or more box plots on the same number line. One representing each set of data. 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 Another is to create histograms with which use the same intervals for both axes. 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 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.

Comparing Types of Peanut Butter 4) Which measure of center and spread would be most appropriate to use to describe these two sets of data? Explain. 5) Compare the two data sets in context. Be sure to address shape, center, spread, and outliers. Which type of peanut butter is better? 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.