Final answer:
For categorical data like car colors, a bar graph is used. Percentiles show how scores compare to a population. A box plot shows data spread and a least-squares line in a scatter plot quantifies relationships between variables like TV size and price.
Step-by-step explanation:
In a situation where you have data on the color of cars driven by students in a statistics class, the appropriate graphical representation would be a bar graph. This is because car colors are categorical data, meaning they represent distinct groups or categories, rather than numerical data that would be represented on a continuum, which is appropriate for a histogram. When discussing percentiles, such as a daughter scoring in the 80th percentile in math, it means she scored the same as or better than 80% of her peers. A percentile rank is a value below which a certain percent of observations fall.
Regarding measures of location of data, the median and the variation are important descriptors. The median is the middle value of a data set, and the variation gives an idea of how spread out the data are. A scatter plot can be used to determine the relationship between two continuous variables, where one variable is considered the independent variable and the other is the dependent variable. A box plot (or box-and-whisker plot) is a graphical representation of a five-number summary: the minimum, first quartile, median, third quartile, and maximum, which is useful for showing the concentration and spread of the data.
Besides providing comparisons among distributions, box plots can also indicate symmetry and skewness within the data, as well as highlight potential outliers. For a detailed analysis of a specific variable, like the size of a television in inches to its sale price, a scatter plot would be employed to visualize the potential relationship, and a least-squares line can be calculated to summarize that relationship quantitatively. The slope of this line represents the change in the dependent variable (sale price) for each unit change in the independent variable (television size).