Question

Town A 16 25 42 38 17 32 42 10 17
Town B 8 0 0 17 30 8 21 9 19
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 summary method:
1. arrange the numbers in each set from least to greatest
2. find the median. for an odd numbered-set it's the number in the exact middle of the list from part 1. for an even numbered set it's the average between the two middle numbers.
3. for each set, take all the numbers below the median (do not include the median itself) and find the median of that set. that becomes your Q1 for each set.
4. for each set, take all the numbers above the median (do not include the median itself) and find the median of that set. that becomes your Q3 for each set.
5. for each set, IQR = Q3 - Q1
6. five number summary: minimum, Q1, median, Q3, maximum
7. make the box plots and check if the plots are symmetrical