Interpreting Categorical and Quantitative Data
PrintInterpreting Categorical and Quantitative Data covers the full pipeline of descriptive statistics. Students represent single-variable data with dot plots, histograms, and box plots; compare center and spread; then move to two-variable data through scatter plots, regression, and two-way frequency tables. A third cluster focuses on interpreting slope, intercept, and correlation coefficients of linear models.
Example Problems
What is the critical value for constructing a 90% confidence interval?
An ornithologist wants to look at the relationship between the breadth of peregrine falcon eggs and the mass of the falcon chicks that hatch from them. The data show a linear pattern with the summary statistics shown below:
Find the equation of the least-squares regression line for predicting the chick's mass from the breadth of the egg, in the form .
Round your entries to the nearest hundredth.
| mean | standard deviation | |
|---|---|---|
| x = egg breadth (mm) | ||
| y = chick's mass (g) | ||
Find the equation of the least-squares regression line for predicting the chick's mass from the breadth of the egg, in the form .
Round your entries to the nearest hundredth.
A tutoring center director wants to look at the relationship between hours of tutoring and final grades. The data show a linear pattern with the summary statistics shown below:
Find the equation of the least-squares regression line for predicting the final grade (points) from the hours of tutoring, in the form .
Round your entries to the nearest hundredth.
| mean | standard deviation | |
|---|---|---|
| = hours of tutoring | ||
| = final grade (points) | ||
Find the equation of the least-squares regression line for predicting the final grade (points) from the hours of tutoring, in the form .
Round your entries to the nearest hundredth.
Identify any outliers from the following table:
| Data Value |
|---|
| 84 |
| 7 |
| 9 |
| 8 |
A fishery biologist recorded the length of trout, in centimeters, and their weight, in grams.
After plotting her results, the biologist noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following least squares regression equation for predicting weight, in grams, from length, in centimeters:
What is the residual for a trout that is long and weighs ?
After plotting her results, the biologist noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following least squares regression equation for predicting weight, in grams, from length, in centimeters:
What is the residual for a trout that is long and weighs ?

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