In the data set below, what are the lower quartile, the median, and the upper quartile?
1 3 3 4 4 6 6 7 8 9
lower quartile =
median =
upper quartile =
To find the lower quartile, median, and upper quartile, we first need to sort the data set in ascending order:
1 3 3 4 4 6 6 7 8 9
Next, we find the median of the entire data set, which is the number that separates the higher half from the lower half. Since there are an even number of values, the median will be the average of the two middle numbers, which are 4 and 6. Therefore, the median is (4 + 6) / 2 = 5.
The lower quartile, also known as the first quartile, is the median of the lower half of the data set. In this case, the lower half without the median consists of 1, 3, 3, and 4. The middle number of this lower half is the median of this quartile, which is (3 + 3) / 2 = 3.
The upper quartile, also known as the third quartile, is the median of the upper half of the data set. In this case, the upper half without the median consists of 6, 6, 7, 8, and 9. The middle number of this upper half is the median of this quartile, which is 7.
Therefore:
Lower quartile (Q1) = 3
Median (Q2) = 5
Upper quartile (Q3) = 7