Part a:
[tex]Q_{1}[/tex] = 56
[tex]Q_{2}[/tex] = 60
[tex]Q_{3}[/tex] = 63
The quartiles are found by finding the medium of the data, and then the mediums of the two different data sets on either side of the medium. The [tex]Q_{2}[/tex] is the overall medium, [tex]Q_{1}[/tex] is the medium of the first half, and [tex]Q_{3}[/tex] is the medium of the second half.
-> How is the medium found? When finding the medium we put the values in order least to greatest and pick the middle value.
[] See attached
Part b:
The range is 7.
The interquartile range is the range of numbers between [tex]Q_{1}[/tex] and [tex]Q_{3}[/tex]. In other words, it is 50% of the data, directly in the middle.
This becomes 63 - 56 = 7
Part c:
79 is an outlier.
It is an outlier because it is 1.5 above or below (in this case, above) the interquartile range.
-> 63 + (7 + [tex]\frac{7}{2}[/tex]) ≤ 79
-> 63 + 10.5 ≤ 79
-> 73.5 ≤ 79
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather
