Free response · Unit 1 Beta

Wait times at two urgent care clinics

Q2: Analyze and interpret data · calculator allowed · 10 points

Share to Google Classroom (opens in a new tab)

The question

Name: ______________________   Date: ____________   Wait times at two urgent care clinics (10 points)

Graph

Wait times at two urgent care clinics

A health network recorded the wait time, in minutes, of 20 randomly selected patients at each of its two urgent care clinics, North and South, during one month (invented data). The boxplots and summary statistics are below.
Summary statistics of wait times (minutes)
ClinicnMeanSDMinQ1MedianQ3Max
North2025.27.81219.524.53041
South2024.516.0813.518.53170
01020304050607080minutesNorthSouth

  1. (a) Compare the distributions of wait times at the two clinics. Address shape, center, variability and unusual features, in context. [4 points]

  2. (b) Use the 1.5 × IQR rule to determine whether the 70-minute wait at South is an outlier. Show your work. [2 points]

  3. (c) One patient waited 35 minutes at North and another waited 40 minutes at South. Calculate the z-score of each wait using the summary statistics, and identify which wait was more unusual for its clinic. [2 points]

  4. (d) A patient wants the better chance of being seen within 20 minutes. Which clinic should the patient choose? Justify your answer using the boxplots or summary statistics. [2 points]