Algebra I, Unit 3

Descriptive Statistics

Overview (Big Ideas):
Students will choose and create an appropriate data representation for a given set of data. They will be able to read and interpret the representations they create as well as others that are given to them. These data representations will include bar graphs, histograms, box-and-whisker plots, stem and leaf plots (including back-to-back stem plots) as well as frequency tables. For categorical data, students will be able to use two-way frequency tables to find joint, marginal and conditional relative frequencies.
Students will calculate and use summary statistics such as mean, median, range, lower and upper quartile, interquartile range and standard deviation to help describe the shape of the data. The processes by which mean and median are calculated have been previously taught. Students have not been introduced to standard deviation, and must understand the process behind the calculation. However, technology should be used to calculate the standard deviation. Students will build on their understanding of these calculations to comment on possible outliers in a data set and to make well-informed decisions about the best summary statistics to represent given data. When data is notably skewed or when meaningful outliers are present, the median and 5-Number Summary should be used to describe the distribution. Alternately, the mean and standard deviation should be used to describe unimodal and symmetric data. Throughout this unit, students should use these summary statistics and/or graphical representations to write critical analyses of a situation within the context of the given data.

Enduring Understandings:
1. Visual displays of categorical and quantitative data should be examined to identify general shape, center and spread.
2. Statistics measuring center and spread can be used to analyze and answer questions about a particular distribution. Appropriate statistics should be chosen based on the general shape of the data.
3. Outliers may affect certain measures of center and spread more than others, which should be taken into account when describing a data set, comparing data sets, or making a decision based on a data set.
4. Sets of data should be compared visually and through the use of descriptive statistics in order to make decisions.


Essential Questions:
  • What are the different methods of data representation and what kinds of data do we use to create them?
  • How can given data representations be interpreted?
  • What are the advantages and disadvantages of each method of data representation?
  • How can data be misrepresented?
  • How can we use summary statistics and data representations to describe a distribution or support or refute a claim?
  • How can understanding statistics and their appropriate use be important and useful to us?

Common Misconceptions:
  • Students often confuse histograms and bar graphs and when to use each.
  • Matching data with an appropriate representation is difficult. Students often try to force data to fit a representation with which they are comfortable.
  • o Students sometimes confuse mean and median.
  • o Box and whisker plots cannot be used to indicate the mean or to indicate sample size.
  • o There are two different types of box and whisker plots offered on most graphing calculators. These are often interchanged and should not be.
  • o Students may merely look for the word “frequency” on a table to tell if it’s a frequency table rather than actually understanding what the data table means and determining whether a frequency is being given.
  • o Students tend to learn quartile data through an algorithm, rather than understanding what it means. This causes difficulty when analyzing box and whisker plots.
  • o Students tend to memorize when to use the mean versus the median due to the presence of an outlier despite several examples given to show the effect on both.
  • o When calculating standard deviation, students may follow a formula or rely on technology rather than understand it. This leads to difficulty analyzing questions about how it can be misused.
  • o Students confuse joint, relative and marginal frequencies.