the box plots below show student grades on the most recent exam compared to overall grades in the class:

two box plots are shown. the top one is labeled class. minimum at 68, q1 at 71, median at 84, q3 at 89, maximum at 100. the bottom box plot is labeled exam. minimum at 55, q1 at 76, median at 85, q3 at 94, maximum at 100.

which of the following best describes the information about the medians?

the class and exam medians are approximately equal.
the class median is much higher than the exam median.
the first quartile for class and exam is the same, but the exam has the lowest median.
the low outlier on exams affects the median significantly.

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

What is the first step of an indirect proof of a number that is divisible by two

What is a possible solutions of the x> 3?