In the data set below, what are the lower quartile, the median, and the upper quartile?
11
13
20
29
31
73
80
84
97
98
99
To find the lower quartile (Q1), the median (Q2), and the upper quartile (Q3) of this data set, we first need to organize the data in ascending order:
11, 13, 20, 29, 31, 73, 80, 84, 97, 98, 99
Now we can find the quartiles:
Since there are 11 data points, the median (Q2) will be the middle value, which is (31).
Q1 is the median of the lower half of the data set, which is the median of the values below 31. Since there are 5 values below 31, Q1 would be the middle value between the 3rd and 4th values: (20 + 29)/2 = 24.5
Q3 is the median of the upper half of the data set, which is the median of the values above 31. Again, there are 5 values above 31, so Q3 would be the middle value between the 3rd and 4th values above 31: (84 + 97)/2 = 90.5
Therefore, the lower quartile (Q1) is 24.5, the median (Q2) is 31, and the upper quartile (Q3) is 90.5.