Question

On San Martin Boulevard, embedded sensors kept track of the vehicle traffic count each hour for five weekdays, Monday through Friday, between 6 a.m. and 8 p.m. (5 weeks × 14 hours = 70 observations).

Answer 1

The question is incomplete. The complete question is below.

On San Martin Boulevard, embedded sensors kept track of the vehicle trafffic count each hour for five weekdays, Monday through Friday between 6am and 8pm. (5 weeks x 14 hours = 70 observations)

(a) Visually estimate the quartiles Q1, Q2, Q3.

(b) Estimate xmin and xmax.

(c) Is the distribution symmetric?

Answer: (a) Q1 = 3300; Q2 = 3900; Q3 = 4300

               (b) xmin = 2400; xmax = 4800

               (c) No

Explanation: The figure below shows a box-and-whisker plot: it is a graphical representation of the variation of data observed through quartiles and lines extending from the lowest and to the highest values.

Quartiles divides a list of numbers into 4 parts (quarters). There are 3 important quartiles:

• Q1: the lower quartile. Represents the left edge of the box;
• Q2: the middle (median) quartile. Corresponds to the median of the set of numbers;
• Q3: the higher quartile. Represents the right edge of the box;

The boxplot also have its minimum and maximum, which is given by the lines (whiskers) of the plot.

Analysing the plot for the San Martin Boulevard:

(a) The lower quartile or Q1 is: Q1 ≈ 3300

The median quartile (Q2) is: Q2 ≈ 3900

The higher quartile (Q3) is: Q3 ≈ 4300

(b) The minimum value the data can assume is: xmin = 2400, while the maximum value is: xmax = 4800

(c) No, the distribution is not symmetric because Q2 is not in the middle of the box and the whisker to the left is longer than to the right. A boxplot is symmetric when median is located in the middle of the box and the whiskers are about the same side on both sides.