In the data set below, what are the lower quartile, the median, and the upper quartile?
16162834545471
lower quartile =
median =
upper quartile =
To find the lower quartile, median, and upper quartile of the data set, we need to first sort the data in ascending order:
1, 1, 4, 4, 5, 7, 6, 8, 1
Next, we need to determine the position of each quartile in the ordered data set:
Lower quartile: (n+1)/4 = (9+1)/4 = 2.5 (average of the 2nd and 3rd values)
Median: (n+1)/2 = (9+1)/2 = 5 (5th value)
Upper quartile: 3*(n+1)/4 = 3*(9+1)/4 = 7.5 (average of the 7th and 8th values)
Therefore, the lower quartile is the average of the 2nd and 3rd values, which is (1 + 4)/2 = 2.5.
The median is the 5th value, which is 5.
The upper quartile is the average of the 7th and 8th values, which is (7 + 8)/2 = 7.5.