Final answer:
To calculate the fraction of patients waiting more than 7 minutes, sum the frequencies for intervals over 7 minutes and divide by the total number of patients. Actual frequencies are not given, so a direct calculation is not possible. Understanding frequency, percentiles, and data interpretation with frequency polygons and box plots is key.
Step-by-step explanation:
To determine the fraction of patients who waited for more than 7 minutes at a dentist's office, we need to look at the frequency distribution of the waiting times for each interval given. Since waiting time intervals are given from 5< x≤6, 6< x≤7, 7< x≤8, 8< x≤9, and 9< x≤10, we need to sum the frequencies of the intervals where time is more than 7 minutes. This includes intervals 7< x≤8, 8< x≤9, and 9< x≤10. Once the frequencies for these intervals are summed, we divide by the total number of patients to get the fraction who waited more than 7 minutes. It is important to note that the actual numbers are not provided in the question, so we cannot compute this directly.
For example, if we assume the frequencies for 7< x≤8 is 'a', for 8< x≤9 is 'b', and for 9< x≤10 is 'c', and the total number of patients is 'N', then the fraction of patients who waited more than 7 minutes would be (a + b + c)/N.
In statistics, understanding the concept of frequency distribution and percentile ranks, such as the 82nd percentile or the 85th percentile, is crucial. Percentiles indicate the percentage of observations that fall below a particular value. For instance, being in the 82nd percentile for waiting times means that 82 percent of patients had shorter wait times, and you waited longer than most. This could be interpreted as a negative outcome in most healthcare service contexts.
Using the concepts of frequency, percentiles, and the interpretation of data through graphs such as frequency polygons and box plots are essential in data analysis. These tools help summarize and understand the distribution of data, which is particularly important in fields like healthcare where service times need to be optimized for patient satisfaction and operational efficiency.