Final answer:
A histogram is a graphical representation of data that helps visualize the distribution by showing frequencies across intervals. For loan applicants, it indicates the years with an employer. If comparing two companies, histograms can reveal which retains workers longer by comparing means and distributions.
Step-by-step explanation:
The student is asking about how to interpret data from a histogram that has been created to summarize the number of years 30 loan applicants have been with their current employer. A histogram is useful in displaying the frequency of data points within certain intervals, which can help visualize the distribution of the data, such as skewness or where the majority of the data points lie.
To answer the student's question, we would explain that a histogram allows us to see the frequency distribution clearly and quickly, by looking at the height of the bars, in which each bar represents a range of years the applicants have been with their current employer. If the bars are mostly on the left side of the histogram, it suggests that most applicants have been with their employer for shorter durations; if they are on the right, longer durations.
If comparing between the histogram data of Company A and Company B from the 'Try It' exercise mentioned, we can determine that Company A tends to retain workers longer than Company B by comparing the means and considering the standard deviations and the overlap in the distributions.
Regarding the decision of graphic representation for the color of cars driven by students, the better choice between a bar graph or a histogram depends on whether the data is categorical (bar graph) or numerical and continuous (histogram).
For percentile scores interpretation, the student's daughter being in the 80th percentile for math means she scored better than 80% of her grade peers, and similarly, a 76th percentile in reading would mean better than 76% of her grade peers.