Find the first and third quartiles, Q1 and Q3, of the following set of numbers.
14, 4, 13, 18, 8, 15, 8, 3, 11, 8
To find the first and third quartiles (Q1 and Q3) of a set of numbers, you need to first arrange the numbers in ascending order.
The given set of numbers is:
4, 8, 8, 8, 11, 13, 14, 15, 18
Step 1: Arrange the numbers in ascending order:
4, 8, 8, 8, 11, 13, 14, 15, 18
Step 2: Calculate the position of Q1 and Q3:
- Q1 is the median of the lower half of the data set.
- Q3 is the median of the upper half of the data set.
There are 9 numbers in the given set, so the median (Q2) will be the middle value, which is the 5th number.
Step 3: Calculate Q1:
- Since there are an odd number of values below Q2, Q1 will be the median of the lower half, excluding Q2.
- The lower half consists of the 4 values: 4, 8, 8, 8.
- The median of the lower half is the middle value, which is the 2nd value.
- Therefore, Q1 = 8.
Step 4: Calculate Q3:
- Since there are an odd number of values above Q2, Q3 will be the median of the upper half, excluding Q2.
- The upper half consists of the 4 values: 13, 14, 15, 18.
- The median of the upper half is the middle value, which is the 2nd value.
- Therefore, Q3 = 14.
So, the first quartile (Q1) is 8 and the third quartile (Q3) is 14.