Question

The following table shows the number of hours some middle school students in two cities spend texting each week: City A 9 27 17 24 21 12 25 25 18 City B 6 20 26 15 23 25 14 14 11 Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (6 points) Part B: Are the box plots symmetric? Justify your answer. (4 points)

Answer 1

Five-number summaries are: lowest value, highest value, upper quartile (Q₃), median (Q₂) and lower quartile (Q₁)

The first step is to rearrange each data set in ascending order as shown in the first diagram

The median (Q₂) of each data set is located on the $5^{th}$ value. 

Once the median is located, we then have the set of data on the left and on the right of median where we are going to locate the Q₁ and Q₃.

Q₁ is located in between the $2^{nd}$ and the $3^{rd}$ value and Q₃ is located between the $7^{th}$ and the $8^{th}$ value.

The box plot of each data set are shown in the second diagram

The box plots aren't symmetric. Box plot for City A tails on the left (negative skew) and box plot for city B also tails on the left (negative skew).