In the data set below, what are the lower quartile, the median, and the upper quartile?
1,2,2,3,3,4,4,5,6,8,9
lower quartile =
median =
upper quartile =
To find the lower quartile, median, and upper quartile, we need to first organize the data in ascending order:
1, 2, 2, 3, 3, 4, 4, 5, 6, 8, 9
Now, we have 11 data points, so the median will be the middle value, which is the 6th value in the ordered list (since 11 is an odd number).
So, the median is 4.
To find the lower quartile (Q1), we need to find the median of the lower half of the data set. In this case, the lower half of the data set is from the 1st value to the 5th value.
So, the lower quartile (Q1) is the median of 1, 2, 2, 3, and 3, which is 2.
To find the upper quartile (Q3), we need to find the median of the upper half of the data set. In this case, the upper half of the data set is from the 7th value to the 11th value.
So, the upper quartile (Q3) is the median of 4, 5, 6, 8, and 9, which is 6.
Therefore:
Lower quartile = 2
Median = 4
Upper quartile = 6