Answer:
Q1 = 13.5
Q3 = 17.5
Step-by-step explanation:
6d) ===============
12, 12, 13, 14, 14, 17, 17, 17, 17, 18, 19, 20
I counted 12 numbers in this set. The median is the middle number of a sorted set. It's also the 2nd quartile as it is 2 quarters in, or 50% in.
First, find the median. In an even-numbered set, that's the average of the 2 middle numbers. In this case, it's between 17 and 17:
12, 12, 13, 14, 14, 17 === 17, 17, 17, 18, 19, 20
Now the set is split into 2 sets with 6 numbers each. Now, find the median of each of those sets. Again, the median of an even-numbered set is the average of the 2 middle numbers.
To find the first quartile (Q1), find the median of the lower set.
12, 12, 13 === 14, 14, 17
The median here is the average of 13 and 14, so 13.5.
6e) ==============
Exactly the same process as above.
7, 12, 12, 13, 14, 14, 17, 17, 17, 18, 19, 20
12 numbers again.
7, 12, 12, 13, 14, 14 === 17, 17, 17, 18, 19, 20
Now, to find the third quartile, find the median of the upper set.
17, 17, 17 === 18, 19, 20
The median is the average of 17 and 18, or 17.5.
