IPS - Day 32

Today we finished looking at rectangle sampling investigation. The sampling techniques used were stratified sampling and cluster sampling.

In looking at stratified sampling, the tendency is for students to just take the 10 rectangles they selected and calculate the average size of the 10. It needs to be emphasized that the two groups are not of equal size and therefore the areas of each rectangle cannot be treated equally. Each rectangle in the first group represents 59% of all rectangles while each rectangle in the second group only represents 41% of all rectangles. We therefore need to calculate a weighted average to account for this difference.

Once students realized this was needed they quickly found their sample, calculated their average rectangle size, and plotted the data on a dot plot. We converted the dot plot to a histogram and discussed the similarities and differences to our simple random sample plot.

The distinguishing characteristics of a stratified sample are noted: the population is broken into groups, the groups must be put together in order to have a complete picture of the population, the size of the groups must be accounted for by weighting in order to keep the sample representative.

We then looked at cluster sampling. Some students needed guidance as to randomization for the sample. In this case the two clusters being selected are selected randomly and then a census is conducted within the two selected clusters. Students generated their data and we looked at the dot plot and histogram.

When comparing the graphs of the simple random samples, the stratified sample, and the cluster sample, students noted that there was less variation in the stratified and cluster samples. They also noted that all four graphs were unimodal and centered near 7. The idea of symmetry and skewness was introduced as students noted the uneven distribution present in a couple of the graphs.

I had the students read through 5 scenarios to check their understanding of the sampling techniques used. Students seemed comfortable with the sampling techniques as almost everyone got all five correct.

For homework, I asked students to conduct a systematic sampling of the rectangles. We'll compare this distribution with the others next class.

Visit the class summary for a student's perspective and to view the lesson slides.