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Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot. These values are used to see how similar other data values are to them.

A box plot can be used to determine how skewed the data is. If the median is roughly in the middle of the box, the data is symmetric. The data is rightskewed if the longer part of the box is to the right of the median. The data is left-skewed if the longer part of the box is to the left of the median.

We are given the below box plot:

Which quarter has the smallest spread of data? What is the spread?

Consider the above box plot:

a) The last 25% spread (Q3 to max) was between 12 and 13.

Which quarter has the largest spread of data? What is the spread?

Consider the above box plot:

b) The second is a 25% spread (Q 1-Q 2), with a range of 2-10.

Find the interquartile range?

Consider the above box plot:

c) $IQR=Q_3-Q_1=12-2=10$

Are there more data in the interval 5-10 or in the interval 10-13? How do you know?

In the range 10-13, there is more information. This interval contains 50% of the data distribution. Since the interval 2-10 contains just 25%, the interval 5-10 will contain less than 25%.

Which interval has the fewest data in it?

Even though it is less than 25%, the interval 2-4 has the smallest proportion of data; it is a subset of the interval 2-10. The data is held in all of the other intervals by a 25%.