Exploring Univariate Data

Students will choose a quantitative variable on which they will obtain two comparable sets of data. (For example, wins for the Dallas Mavericks versus wins for the San Antonio Spurs over the last 25 seasons.) Students will obtain the data and analyze its type and whether it’s random or representative. Students will then create graphical displays to help convey the concept of shape of a distribution. Then students will then move into the numerical analysis of center and spread and include a written comparison of these characteristics for the two data sets. Students will conclude with an overall conclusion about the compared data sets.

Subject/Course:

Math

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Significant Content

Obtaining different types of data; Calculating measures of central tendency and dispersion; Creating graphical displays of univariate data; Comparing 2 sets of univariate data.

21st Century Competencies

Collaboration:

Students may choose a partner and then complete a partner evaluation on his/her contribution.

Communication:

Students may present their findings in written or oral form.

Critical thinking:

Critical Thinking

Creativity and innovation:

Students may choose any form of media to present their findings

Driving Question

How do you compare two different univariate quantitative data sets?

Entry Event

Do girls take longer than boys to get ready in the morning? As a class, the students will gather their own “get ready time” and compare the data sets of get ready times for boys and girls.

Products

Individual:

Graphs, Calculated statistics, written comparisons

Team:

Oral presentation of their project findings

Specific content and copetencies to be assessed:

Correct calculations, graph constructions, and comparisons.

Resources Needed

On-site people facilities:

Depending on project design, may need access to a sample pool of people.

Equipment:

Computer lab, web access for data gathering.

Learning outcomes targets:

I can identify the attributes of my data set including the population and sample and whether the data is discrete or continuous.

I can create frequency distributions including dot plots, tables, frequency histograms with equal class intervals, and box-and-whisker plots

I can calculate or find statistical measures of central tendency (mean, median, mode) and dispersion (range, IQR, variance, standard deviation, outliers) and their interpretations.

I can make direct comparisons of the shapes, centers, and spreads of two data sets.

Checkpoints formative assessments:

1. Exit ticket describing project plan and data sets to be explored. 2. Journal entry describing how data will be obtained.

1Journal entry describing how the graphs are going to be created – by hand, software, etc. 2. Activity on interpreting different features of frequency distributions.

1.Quiz on calculating statistical measures.

1Activity matching shapes with different statistical measures. 2. Exit ticket describing how students know which measures to use when comparing data sets.

Instructional strategies for all learners:

Brainstorming activity for quantitative data that could be obtained by students from students about students. Class discussion about the best methods for obtaining data and what the responses might include.

Class activity using real data to create models with different shapes. Teacher may model the techniques for creating the different graphical displays. Notes can be used as supplemental instruction for the construction of the displays.

Teacher model – class demonstration of finding measures using the calculator.

Teacher emphasizes using direct comparative words (higher, lower, greater, less) about the 3 characteristics.

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