The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. What are the first and third quartiles?(1 point)
First Quartile:
Third Quartile:
To find the first and third quartiles, we need to divide the list of prime numbers into four equal parts.
First, we need to find the median of the given prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Since this list has an even number of terms, the median is the average of the middle two terms: (7 + 11) / 2 = 18 / 2 = 9.
Next, we divide the list into two halves: one from the beginning up to the median, and the other from the median to the end:
First half: 2, 3, 5, 7
Second half: 13, 17, 19, 23, 29
Now, let's find the median of each half:
First half: 2, 3, 5, 7
Median = (3 + 5) / 2 = 8 / 2 = 4
Second half: 13, 17, 19, 23, 29
Median = 17
The first quartile is the median of the first half, which is 4, and the third quartile is the median of the second half, which is 17.
First Quartile: 4
Third Quartile: 17
To find the first and third quartiles of a set of numbers, you need to arrange them in ascending order.
The given set of numbers in ascending order is: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
First, find the median (Q2) of the entire set:
- There are 10 numbers, so the median is the average of the 5th and 6th numbers.
- The 5th number is 11, and the 6th number is 13.
- Therefore, the median (Q2) is 11 + 13 / 2 = 12.
Now, find the median (Q1) of the lower half of the set:
- The lower half consists of the numbers before the median (Q2).
- The lower half is: 2, 3, 5, 7.
- There are 4 numbers, so the median (Q1) of the lower half is the average of the 2nd and 3rd numbers.
- The 2nd number is 3, and the 3rd number is 5.
- Therefore, the median (Q1) of the lower half is 3 + 5 / 2 = 4.
Lastly, find the median (Q3) of the upper half of the set:
- The upper half consists of the numbers after the median (Q2).
- The upper half is: 13, 17, 19, 23, 29.
- There are 5 numbers, so the median (Q3) of the upper half is the average of the 3rd and 4th numbers.
- The 3rd number is 17, and the 4th number is 19.
- Therefore, the median (Q3) of the upper half is 17 + 19 / 2 = 18.
So, the first quartile (Q1) is 4, and the third quartile (Q3) is 18.