Math 1 · Unit 12 · Lesson 5

Comparing Data Sets

Five steps to compare groups: graph them on the same scale, describe each shape, choose the statistics that fit the shape and use the same kind for both, compare centers and spreads, and write sentences in context. Two Math 1 classes have almost the same mean, but one is skewed with an outlier, so the median and IQR tell the real story: 1st period scored higher and 4th period was more consistent. Then Delia's three fertilizers.

About 45 minutes Higher, and more consistent?

The big idea

Comparing groups is the whole unit in order: graph them on the same scale, describe each shape, choose the statistics that fit the shape and use the same kind for every group, compare centers and spreads, and write sentences in context. The shape picks the statistics: the mean and standard deviation for roughly symmetric data with no outliers, the median and IQR for skewed data or data with outliers. Two classes with means of 83.3 and 83 look the same by the mean alone, but 1st period is skewed left with an outlier at 34, so the median and IQR are the right numbers, and they show 1st period scoring higher (87.5 against 83) while 4th period was far more consistent (IQR 5 against 12.5). A whole class is a population, so sigma is the standard deviation to use. The same five steps pick a fertilizer that grows seedlings both tallest and most evenly, and because the standard deviation is in the data's own units, it lets you compare spread even across different kinds of measurements.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2Five steps, and two classes with the same meanEverything in this unit comes together when you compare two or more groups. 3Delia's fertilizers, and spread in different unitsDelia tested three fertilizers on tomato seedlings, ten seedlings each, and measured the heights in... 4Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the five steps, the two classes with the model answer, the sentence frame, Delia's fertilizers, and spread across units. Plus a worksheet with an answer key and a short lesson plan.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: Outliers and What They DoThe 1.5 IQR rule. Coming next: Unit 13, Properties of ExponentsWhy multiplying powers adds exponents, why anything to the zero power is 1, and how square roots connect to exponents. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.

NC Math 1 standards in this lesson: NC.M1.S-ID.2 (compare center and spread of two or more data sets with statistics that fit the shape, in context), NC.M1.S-ID.3 (outliers and shape in the comparison).