Five number summary and box plots

Today's focus was the five number summary and box plots. The class seemed to do okay with finding a data set that had specific means and standard deviations. Most are getting more adroit at using their calculators to assist them with their calculations and analysis.

We then used the data from the two data sets we used last week to calculate mean and standard deviation and focused on finding the five number summary and IQR. This lesson went much as planned. I was hoping to discuss the connections between sampling, estimating using sample statistics, and the population statistics we are seeking to understand. That discussion will have to wait until tomorrow.

Below is the  lesson outline with comments italicized between square brackets, [like this].

o   What is a quartile?

§  Discuss

o   How can we divide a data set into quartiles?

§  Find median then find median of lower and upper halves

§  Use height data on board to illustrate [Used data from two sets that worked on last class for mean and standard deviation.]

o   Range is difference between max and min, we could look at the difference between Q3 and Q1 [Discussed issues with  range, specifically outliers.]

o   IQR = Q3 – Q1, describes spread of middle 50% of data, it’s another measure of spread

    [Asked class to consider what other ways could measure spread. There were a few ideas suggested that were a bit more involved but could work. Students also confirmed that we wanted to make use of 5-number summary data as the basis for the spread measurement. I was pleased that these students were focused on the proper things.]

o   Box plot

§  Create box on a scale (vertical or horizontal)

§  What about whiskers?

§  Define upper and lower limits using Q1 – 1.5IQR and Q3 + 1.5IQR

§  Whisker goes to actual point values within limits

§  All values outside limits are marked with asterisk and denoted as an outlier [There were good clarifying questions at this point and we spent some time on these. The second data set was used as practice. Afterward, I showed the class how the graph could be constructed using their graphing calculators.]

o   You report summary statistics for your sample, either mean and standard deviation or 5# summary and IQR.

§  Mean and standard deviation used for roughly symmetric data

o   Create 5# summaries and box plots for the two data sets

§  Share and discuss [Put both box plots on the same scale. Discussed ways to compare and contrast the graphs. Discussed what the means in drawing conclusions about the  two data sets.]

o   Complete river sampling questions

§  Share and discuss [This piece went  a little longer than planned. Students were grouped into three sets of 10-12 students as they shared data. They had four box plots to create along with summary statistics for the four data sets. They then had to write a few sentences comparing the graphs. I told the class that anyone can see the graphs, the comparison is what they want people to focus on that will justify their conclusion. I'll have students share what they wrote next class and then we'll focus on the issue of always discussing shape, center, and spread.]