They have different ranges. In other words, their differences between the highest and lowest values are different.
Let's say that each of the sets will have seven elements. Also, we will write them in an ordered form from least to greatest.
& , , , , , ,
& , , , , , ,First, note that the median and quartiles are all about the placement of values in an ordered data set. Median is the middle value of the set.
Median
↑
a b c^(Lower half) d e f g^(Upper half)
If there was an even number of data points, then it would be the average of the two middle values. Now, quartiles Q_1 and Q_3 are the middle values of the lower and upper half of the set.
Median
↑
a b c^(Lower half) d e f g^(Upper half)
↓ ↓
Q_1 Q_3
Same as before, if the halves consisted of an even number of points, each quartile would be an average of the two middle values. Let's now choose these three values. They will be the same for both sets, as required.
& , 4, , 7, , 11,
& , 4, , 7, , 11,
Now, there are infinitely many numbers that we can write in the remaining gaps. The only restriction is that the ranges of the sets should be different. Let's fill in the gaps!
& , 4, 5, 7, 9, 11, 15
& 2, 4, 6, 7, 10, 11, 12
The range of the first set is 15-0=15. The range of the second set is 12-2=10. Since 15 ≠10, the ranges are different our sets meet all the conditions.
