Find the minimum, first quartile, median, third quartile, and maximum of the data set below.
4.7
3.4
6.4
4.6
4.8
4.9
5.9
4.2
12.3
To find the minimum, first sort the data set in ascending order:
3.4, 4.2, 4.6, 4.7, 4.8, 4.9, 5.9, 6.4, 12.3
The minimum value is 3.4.
The first quartile (Q1) is the median of the lower half of the data set. Since there are 9 data points, the lower half consists of the first 4 numbers:
3.4, 4.2, 4.6, 4.7
The median of this lower half is the average of the two middle values:
(4.2 + 4.6) / 2 = 4.4
The first quartile is 4.4.
The median is the middle value of the sorted data set. In this case, since there are 9 data points, the median is the value in the 5th position:
4.8
The third quartile (Q3) is the median of the upper half of the data set. Again, since there are 9 data points, the upper half consists of the last 4 numbers:
4.8, 4.9, 5.9, 6.4
The median of this upper half is the average of the two middle values:
(4.9 + 5.9) / 2 = 5.4
The third quartile is 5.4.
The maximum value is the largest value in the data set:
12.3
So, the minimum is 3.4, Q1 is 4.4, the median is 4.8, Q3 is 5.4, and the maximum is 12.3.