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Answer: Part A. The IQR for town A is 4.5 and the IQR for town B is 4.5
Part B. No, they are assymetric.
Explanation: To find the interquatile range (IQR) of each set of data, you can do as follows:
1) Put the number in each set of data in order:
A: 3 4 5 5 6 7 8 9 9 20
B: 3 3 5 5 6 8 8 9 9
2) Find the median of each town data:
For A, the median is the number 6. Coincidently, the same can be said for town B: its median is 6.
3) Find Q1, which is the median (or the middle term) of the left side of the median:
A: 3 4 5 5 (set of numbers to calculate)
B: 3 3 5 5
Now, as both set of number are even, to find the median, we have to calculate the mean of the two central numbers:
For A: Q1 = = 4.5
For B: Q1 = = 4
4) Find Q3, which is the median of the right side of the first median:
A: 7 9 9 20 (set of numbers to calculate)
B: 8 8 9 9
As before, the median will be the mean:
For A: Q3 = = 9
For B: Q3 = = 8.5
5) The IQR is the result of a subtraction:
IQR = Q3 - Q1
For A: IQR = 4.5
For B: IQR = 4.5
For the two sets of data the IQR is the same and equals 4.5.
Part B: Box plot is a type of graphic, similar to histogram. To plot it, you need 5 points but for this question, it will be analised just the symmetric aspect. As the graphic is a retangule, to be symmetric, the median or mean has to be in the center of the retangule. In the case of the towns, the box plots are assymetric because the median of each town is closer to the Q1 of each town. In other words, the retangule is not "divided" exactly in half.