Final answer:
To find the third quartile among the numbers 10, 17, 32, 16, 18, 20, first arrange them in ascending order, identify the median, and then find the median of the upper half. The third quartile (Q3) for this set of numbers is 20.
Step-by-step explanation:
Finding the Lower Quartile (Q3)
To determine the third quartile (Q3), also known as the upper quartile, among a set of numbers, one must follow a series of steps which include organizing the data in ascending order and then dividing the dataset into four equal parts. Given the numbers 10, 17, 32, 16, 18, 20, we must first arrange them from smallest to largest: 10, 16, 17, 18, 20, 32. Since we have an even number of observations, the median (Q2) falls between the third and fourth values, which are 17 and 18. In this case, the median is the average of 17 and 18, giving us 17.5.
The upper half of the data, which consists of the numbers larger than the median, is 18, 20, and 32. The median of this upper half is the value that separates the higher half into two equal parts. Since we have only three numbers in the upper half, the middle value is also the median of the upper half, which in this case is 20. Therefore, the lower quartile (Q3) among the given numbers is 20.