S-ID: Interpreting Categorical and Quantitative Data

Interpreting Categorical and Quantitative Data

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Interpreting Categorical and Quantitative Data covers graphical displays of distributions including dot plots, histograms, and box plots, alongside measures of center and spread. Categorical data is analyzed in two-way frequency tables, and scatter plots support linear regression with correlation coefficients. Correlation versus causation is a key interpretive distinction throughout.

S-ID.1Represent data with plots on the real number line (dot plots, histograms, and box plots).S-ID.2Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.S-ID.3Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). For example: Justify why median price of homes or income is used instead of the mean.S-ID.4Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.S-ID.5Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.S-ID.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.S-ID.7Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.S-ID.8Compute (using technology) and interpret the correlation coefficient of a linear fit.S-ID.9Distinguish between correlation and causation.
Example Problems
The delivery time (in days) for a regional courier is normally distributed with a mean of and a standard deviation of . Let = the delivery time for a randomly selected package.

Find
.
Round your answer to
two decimal places.
What is the average value of on the interval ?
Identify any outliers from the following table:
Data Value
84
7
9
8
What is the critical value for constructing a 90% confidence interval?
A bookstore surveyed customers on preferred book format.

FormatHardcoverPaperbackeBook
Students203545
Adults504010


How many students prefer
eBooks?
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