Statistics and Probability

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Understand that both a measure of center and a description of variability should be considered when describing a numerical data set.

Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. o Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. o Understand the median as a measure of center that is the numerical middle of an ordered data set.

Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads.

Display numerical data in plots on a number line. • Use dot plots, histograms, and box plots to represent data. • Compare the attributes of different representations of the same data.

Summarize numerical data sets in relation to their context.

Describe the collected data by: o Reporting the number of observations in dot plots and histograms. o Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement.

Analyze center and variability by: o Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. o Justifying the appropriate choice of measures of center using the shape of the data distribution.