The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. What are the first and third quartiles?
To find the first and third quartiles, we need to first find the median of the data set.
The median of the first five prime numbers (2, 3, 5, 7, and 11) is 5.
The median of the first ten prime numbers is the average of the fifth and sixth primes (11 and 13), which is 12.
To find the first quartile, we need to find the median of the first five prime numbers (2, 3, 5, 7, and 11). The median of this subgroup is 5.
To find the third quartile, we need to find the median of the second subgroup of five prime numbers (13, 17, 19, 23, and 29). The median of this subgroup is 19.
Therefore, the first quartile is 5 and the third quartile is 19.
To find the first and third quartiles of a set of numbers, follow these steps:
Step 1: Arrange the numbers in ascending order:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Step 2: Calculate the median:
Since there is an even number of numbers (10 in this case), the median is the average of the two middle numbers. The two middle numbers in this case are 7 and 11. So the median is (7 + 11) / 2 = 9.
Step 3: Divide the numbers into two halves:
The first half of the numbers will be: 2, 3, 5, 7, 9
The second half of the numbers will be: 13, 17, 19, 23, 29
Step 4: Find the median of the first half:
Since there are 5 numbers in the first half, the median will be the middle number, which is 5.
Step 5: Find the median of the second half:
Since there are 5 numbers in the second half, the median will be the middle number, which is 19.
Therefore, the first quartile is 5, and the third quartile is 19.