Question:
The box plots below show student grades on the most recent exam compared to overall grades in the class: two box plots shown. The top one is labeled Class. Minimum at 70, Q1 at 74, median at 83, Q3 at 92, maximum at 100. The bottom box plot is labeled Exam. Minimum at 60, Q1 at 81, median at 87, Q3 at 91, maximum at 95. Which of the following best describes the information about the medians? (1 point) Group of answer choices
•The exam outlier at 60 makes the IQR narrower and the median higher.
•The class data is more evenly spread, which pulls its median down.
•The class median is lower than the exam median.
•The class Q3 is higher than the exam Q3.
Answer:
•The class Q3 is higher than the exam Q3.
Step-by-step explanation:
In the question we have two box plots
a) Box plots for class is given as
Minimum at 70, Q1 at 74, median at 83, Q3 at 92,
b) Box plots for exam is given as Minimum at 60, Q1 at 81, median at 87, Q3 at 91, maximum at 95.
When we compare the median of the class which is 83 and the median of the exam plots 87, we can see that the median of the exam is higher than the median of the class, hence the option
"•The class median is lower than the exam median". is wrong.
From the options given, the only correct option which best describes the information about the medians is
"•The class Q3 is higher than the exam Q3".
This is because when we compare the Q3 of the class which is 92 to the Q3 of the box which is 91 , we can see that the class Q3 is higher than the box Q3 hence the option is correct.
where b is the upper bound and a is the lower. For us, this formula will be filled in accordingly. 
. We will integrate that now: ![\frac{1}{2}[ \frac{2x^3}{3}+3x]](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%5B%20%5Cfrac%7B2x%5E3%7D%7B3%7D%2B3x%5D%20%20)
from 0 to 2. Filling in our upper and lower bounds we have ![\frac{1}{2}[( \frac{2(2^3)}{3}+3(2))-0]](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%5B%28%20%5Cfrac%7B2%282%5E3%29%7D%7B3%7D%2B3%282%29%29-0%5D%20%20)
which simplifies to 
and 
which is 17/3 or 5.667