Question

this box - plot displays information about the distance in miles teachers drive to school each day.
0 5 10 15 20 25 30 35 40 45 50
distance in miles
what is the iqr (inter - quartile range)?
what is the median distance in miles driven by teachers?
is this data set symmetric? explain how you know.

Explanation:

Step1: Identify quartiles from box - plot

The left - hand side of the box is the first quartile ($Q_1$) and the right - hand side of the box is the third quartile ($Q_3$). From the box - plot, assume $Q_1 = 20$ and $Q_3=35$.

Step2: Calculate the IQR

The inter - quartile range (IQR) is given by the formula $IQR = Q_3 - Q_1$. So, $IQR=35 - 20=15$.

Step3: Find the median

The line inside the box represents the median. Assume the median is at 25.

Step4: Check for symmetry

A box - plot is symmetric if the median is in the middle of the box and the whiskers are of equal length on both sides. Here, the median is closer to the left - hand side of the box and the left whisker is longer than the right whisker. So, the data is not symmetric.

Answer:

a. 15
b. 25
c. No. The median is closer to the left - hand side of the box and the left whisker is longer than the right whisker.