Samples and Populations: Making Comparisons and Predictions
The Process of Statistical Investigation: Understand and use the process of statistical investigation.
- Pose questions, collect and analyze data, and make interpretations to answer questions
- Apply Guidelines for Describing Distributions as a tool to be used with the analyzing and interpreting phases of the statistical investigation process
- Construct and use simple surveys as a method of collecting data
Analysis of Data Distributions: Understand data distributions and what it means to analyze them.
- Distinguish data and data types
- Recognize data consist of counts or measurements of a variable that are called a distribution of data values
- Distinguish between categorical data and numerical data and identify which graphs and statistics may be used to represent each kind of data
- Use multiple representations
- Organize and represent data using tables, dot plots, line plots, value bar graphs, frequency bar graphs, histograms, and box-and-whisker plots
- Make informed decisions about which graphs/tables are used to display data being analyzed (ties back to questions asked, data types, etc.)
- Recognize that data displayed using a graph shows the overall shape of a distribution and gives a general sense of whether the data values are or are not symmetrical around a central value or if there is something unusual about the shape
- Recognize that a single number may be computed and used to characterize the center or what's typical for a distribution of data
- Distinguish and compute measures of central tendency: the mean, median, or mode of the data
- Identify how the median and mean respond to changes in the number and magnitude of data values in a distribution
- Make informed decisions about which measures of central tendency (mean, median, or mode) may be used to describe a data distribution
- Recognize that variability occurs whenever data are collected and describe the variability in the distribution of a given data set
- Describe the amount of variability in a distribution, noting if the data values are pretty much the same or are quite spread out
- Distinguish and compute measures of spread: range, interquartile range (IQR), and mean absolute deviation (MAD)
- Develop strategies for analyzing and/or comparing data distributions
- Identify which statistical measures of center and spread (mean, median, mode, range, etc.) are most appropriate to use to describe a distribution of data
- Use measures of center and spread to compare data distributions
Representative Samples: Understand that statistics can be used to gain information about a population by examining a representative sample of the population.
- Use random sampling to select representative samples and use data from these samples to draw conclusions about populations
- Explore the influence of sample size and sample selection processes on measures of center and variability that describe a sample distribution
- Apply concepts from probability to select random samples from populations
- Compare sample distributions using measures of center (mean, median), measures of spread (range, IQR, MAD), and data displays that group data (histograms, box-and-whisker plots)
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